The Theory and Applications of the Inners

Proceedings of the IEEE

Volumn 63, Issue 7, 1975, Pages 1044-1068

  Jury, E I ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

INNERS;

MATHEMATICAL TECHNIQUES;

EID: 0016535608     PISSN: 00189219     EISSN: 15582256     Source Type: Journal    
DOI: 10.1109/PROC.1975.9880     Document Type: Article

References (177)

1. E L Jury, “On a positive innerwise matrix (Part I),” Electron. Res. Lab., Univ. of California, Berkeley, Internal Memo, Apr. 1970
2. —, “ ‘Inners’ approach to some problems of system theory,” IEEE Trans. Automat. Contr., vol. AC-16, pp. 233–240, June 1971
3. —, Inners and Stability of Dynamic Systems. New York: Wiley, 1974
4. J. Sylvester, “A method of determining by mere inspection the derivatives from two equations of any degree,” Phil. Mag., vol. XVI, pp. 132–135, 1840; also Collected Math. Papers, i, pp. 54–57. 57
5. N. Trudi, Teoria di Deterministi e Loro Applicacioni, D. B. Pellerano, Ed. Naples, Italy: Libreria Scientifica e Industriale, 1862
6. A. Rowe, “The generalized resultant matrix,” J. Inst. Math. Its Appl., vol. 9, pp. 390–396, 1972
7. E. Netto, “Zur Theorie der Resultaten,” J. Reine Angew. Math., vol. 116, pp. 33–49, 1896; vol. 117, pp. 57–71, 1897
8. E. H. Bareiss, “Resultant procedure and the mechanization of the Graeff process,” Int. Ass. Comput Mach., vol. 7, pp. 346-386, 19 6 0
9. M. P. Epstein, “The use of resultants to locate extreme values of polynomials,” SIAM J. Appl. Math., vol. 16, pp. 62–70, 1968
10. T. Muir, The Theory of Determinants in Historical Order of Developments. vols. I-IV. New York: Dover, 1960
11. S. Y. Ku and R. J. Adler, “Computing polynomial resultants: Bezout's determinant vs. Collins’ reduced P. R. S. algorithm,” Commun. Ass. Comput. Mach., vol. 12, pp. 23–30, Jan. 1969
12. A. T. Fuller, “Stability criteria for linear systems and realizability criteria for RC networks,” Proc. Cambridge Phil. Soc., vol. 53, pp. 878–896, 1957
13. —, “Conditions for aperiodicity in linear systems,” Brit. J. Appl. Phys., voL 6, pp. 195–198, 1955
14. A. Liénard and M. H. Chipart, “Sur la signe de la partie reelle des racines d'une équation algebrique,” J. Math. Pure Appl., vol. 10, pp. 291–346, 1914
15. A. S. Householder, “Bigradients and the problem of Routh and Hurwitz,” SIAM Rev., vol. 10, 56–66, 1968
16. A. S. Householder, “Bigradients, Hankel determinants, and the Padé table,” in Constructive Aspects of the Fundamental Theorem of Algebra, B. Dejon and D. Hermichi, Eds. New York: Wiley-Interscience, 1969
17. A. S. Householder “Bezoutians, elimination and realization,” SIAM Rev., vol. 12, pp. 73–78, 1970
18. M. Uruski, and M. S. Peikarski, “Synthesis of a network containing a cascade of commensurate transmission lines and lumped elements,” Proc. Int. Elec. Eng., vol. 119, pp. 153–160, Feb. 1972
19. H. H. Rosenbrock, State-Space and Multivariable Theory. London, Nelson, 1970
20. P. C. Müller, “Solution of the matrix equations AX + XB =-a and S T X + XS =-a,” SIAM J. Appl. Math., vo L 18, pp. 682–687, 687, May 1970
21. R. E. Hartwig, “The resultant and the matrix equation AX = XB,” SIAM J. Appl. Math., vol. 22, pp. 538–544, June 1972
22. R. E. Hartwig, “Resultants and the solution of AX-XB =-C,” SIAMJ. Appl. Math., vol. 23, 104–117, July 1972
23. S. Barnett, Matrices in Control Theory. Princeton, N. J.: Van Nostrand, ch. 2, 1971
24. E. I. Jury, “A simplified stability criterion for linear discrete systems,” Proc. IRE, vol. 50, p p. 1493–1500, June 1962
25. —, “On the evaluation of the stability determinants in linear discrete systems,” IRE Trans. Automat. Contr., voL AC-7, pp. 1962
26. E. L Jury and J. Blanchard, “A stability test for linear discrete systems i n table form,” Proc. IRE, vol. 49, pp. 1947–1948, Dec. 1961
27. E. L Jury, “A stability test for linear discrete systems using a simple dimension,” Proc. IRE, vol 49, pp. 1948–1949, Dec. 1961
28. C. Hermite, “Sur le nombre des racines d'une ëquation algëbrique comprise des limites données,” J. Reine Angew. Math., vol. 52, pp. 39–51, 1854
29. E J. Routh, A Treatise on the Stability of a Given State of Motion. London, England: Macmillan, 1877
30. A. Hurwitz, “Über die Bedingungen unter welchem eine Gleichung chung nur wurzeln mit negativen relen Teilen besitzt,” Math. Ann., VOL 46, pp. 273–284. 1895
31. L. A. Zadeh and C. A. Desoer, Linear System Theory the State Space Approach, New York: McGraw-Hill, 1963, p. 419
32. I. Schur, “Über Potenzreihen, die i n Inners des Einheitskreises beschrankt sind,” J. Für Math., vol. 147, pp. 205–232, 1917
33. A. Cohn, “Über die Anzahl der Wurzeln einer algebraischen Gleichung in einen kreise,” Math. Z., vols. 14–15, pp. 110–148, 1922
34. E. L Jury, “Proof of a general relationship used in the stability test of linear discrete systems,” an addendum to [24]; Inst. Eng Research, Ser. no. 60, Dec. 1961
35. B. D. O. Anderson and E. I. Jury, “A simplified Schur-Cohn test,” IEEE Trans Automat. Contr., voL AC-18, pp. 157–163, Apr. 1973
36. E. I. Jury and S. M. Ahn, “Symmetric and innerwise matrices for the root clustering and root-distribution of a polynomial,” J. Franklin Inst., vol. 293, pp. 433–450, June 1972
37. F. R. Gantmacher, Theory of Matrices vol. IL New York: Chelsea, 1959, ch 5
38. A. A. Markov, Collected Works. Moscow, USSR, 1948
39. A. M. Lyapunov, Le Probléme Générale de la Stabilité du Mouvement. Princeton, N. J.: Princeton Univ. Press, 1949
40. M. Marden, Geometry of Polynomials, 2nd ed. Providence, R. I.: Amer. Math. Soc., 1966
41. R. K. Sharma and E. L Jury, “Inner-Minor transformation,” IEEE Trans. Automat. Contr., voL AC-18, pp. 75–76, Feb. 1973
42. B. D. O. Anderson and E. I. Jury, “On the reduced Hermite and reduced Schur-Cohn metric relationships,” Int. J. Contr., vol. 19, no. 5, pp. 877–890, 1974
43. B. D. O. Anderson, N. K. Bose, and E. I. Jury, “A simple test for zeros of a complex polynomial in a sector,” IEEE Trans. Automat. Contr., vol. AC-19, pp. 437–438, Aug. 1974
44. M. R. Stoji ć and D. D. Siljak, “Generalization of Hurwitz, Nyquist, Mikhailov stability criteria,” IEEE Trans. Automat. Contr., vol. AC-10, pp. 250–254, July 1965
45. M. V. Meerov, “Criteria of aperiodic systems,” Izv. Akad. Nauk SSSR, OTN, no. 12, p. 1169, 1945
46. M. I. Romanov, “Algebraic criteria for aperiodicity of linear systems,” Doki. Akad. Nauk SSSR, vol. 12f, no. 2, pp. 291–294, 1959
47. B. D. O. Anderson, E. I. Jury, and F. L. C. Chapparro, “Relations between real and complex polynomials for stability and aperiodicity conditions,” IEEE Trans. Automat. Contr., vol. AC-20, pp. 244–246, Apr. 1975
48. E. L Jury and J. Tschauner, “On the inners formulation of stability condition within the shifted unit circle,” Regelung stechnik, vol. 7, pp. 299–300, July 1971
49. E. L Jury, “Stability, root clustering and inners,” in Proc. 1972 IFAC Cong
50. R. Courant and D. Hilbert, Methods of Mathematical Physics. New York: Interscience, vol. II, 1962
51. E. I. Jury and S. M. Ahn, “The theory of inners as applied to networks,” in 1970 IEEE Int. Symp. Circuit Theory, Dig. Tech. Papers, pp. 183–184
52. E. I. Jury, “Physical realization of the impedance function of short-circuited cascade of uniform lossless transmission lines (SCULL),“ IEEE Trans. Circuit Theory, vol. CT-19, pp. 100–103, 103, Jan. 1972
53. ——, “Remarks on ‘physical realization of the impedance function of short-circuited cascade of nonuniform lossless transmission lines (SCULL)’ “, IEEE Trans. Circuits and Systems, vol. CAS-21, pp. 459–461, May 1974
54. B. K. Kinariwala and A. Gersho, “A stability criterion for nonuniformly uniformly sampled and distributed parameter systems,” Bell Syst. Tech. J., p. 1153, Sept. 1966
55. M. R. Clark, U. U. Krishnan, and L. Stark, “An initial application of inners to bioengineering models,” in Symp. Rec. Int. Symp. Circuits and Systems, pp. 22–25, Apr. 1974
56. ——, “Inners and bioengineering models,” Bull. Math. Biol., 1975
57. R. E. Kalman, “Algebraic characterization of polynomials whose zeros lie in a certain algebraic domain,” Proc. Nat. Acad. Sci. U. S., vol. 64, pp. 818–823, 1969
58. E. I. Jury and S. M. Ahn, “Remarks on the root-clustering of a polynomial in a certain region in the complex plane,” Quart. Appl. Math., vol. XXXII, pp. 203–205, July 1974
59. J. L. Howland, “Matrix equations and the separation of matrix eigenvalues,” J. Math. Anal. Appl., vol. 33, pp. 683–691, 1971
60. R. D. Hill, “Inertia theory for simultaneously triangulizable complex matrices,” in Linear Algebra and Its Applications, 1969, pp. 131–142
61. E. L Jury, “On positive innerwise and positive definite symmetric matrices,” to be published
62. M. Mansour, Stability Criteria of Linear Systems and the Second Method of Lyapanov. Zürich, Switzerland: Scientia, 1965
63. P. Parks, “A new proof of the Hurwitz stability criterion by the second method of Lyapanov with applications to optimum transfer functions,” in 1963 4th Joint Automat. Contr. Conf., June
64. M. Mansour, “Stability of linear discrete systems and the second method of Lyapunov,” Regelungstechnik, 1965
65. A. J. Berkhout, “Stability and least-squares estimation,” to be published
66. T. Kailath, “A view of three decades of linear filtering theory,” IEEE Trans. Inform. Theory, vol. IT-20, pp. 146–181, Mar. 1974
67. N. Levinson, “The Wiener rms error criterion in filter design and prediction,” J. Math. Phys., vol. 25, pp. 261–278, 1947
68. L. Orlando, “Sul problema di Hurwitz relativo all parti reali dell vadici di un'equatione algebrica,” Math. Ann., vol. 71, pp. 233–245, 245, 1911
69. S. Barnett, “Application of the Routh array to stability of discrete-time linear systems, Int. J. Contr., vol. 19, no. 1, 47–55, 1974
70. O. Brune, “Synthesis of a finite two-terminal network whose driving point impedance is a prescribed function of frequency,” J. Math. Phys., vol. 10, pp. 191–236, Oct. 1931
71. E. A. Guillemin, Synthesis of Passive Networks. New York: Wiley, 1957, ch. 1
72. L. Weinberg, Network Analysis and Synthesis. New York: McGraw-Hill, 1962, pp. 257–269
73. D. D. Åiljak, Nonlinear Systems. New York: Wiley, 1969, pp. 352–367
74. D. D. Å iljak, “New algebraic criteria for positive realness,” J. Franklin Inst., vol. 291, pp. 109–120, Feb. 1971
75. M. V. Meerov, “Analytical conditions for positivity of a real function,” Dokl. Akad. Nauk SSSR, vol. 165, pp. 780–782, 1965
76. D. D. Å iljak, “Algebraic criterion for absolute stability, optimality and passivity of dynamic systems,” Proc, Inst. Elec. Eng., vol. 117, Oct. 1970
77. R. E. Kalman, “When is a linear control system optimal?,” J. Basic Eng. ASME, vol. 86, pp. 51–60, Mar. 1964
78. V. M. Popov, “Incompletely controllable position systems and application to optimization and stability of automatic control systems,” Rev. Roum. Sci. Tech. Ser. Electrotech. Energ., 1967
79. R. N. Gadenz and C. C. Li, “On positive definiteness of quartic forms of two variables,” IEEE Trans. Automat. Contr., vol. AC-9, pp. 187–188, Apr. 1964
80. W. H. Ku, “Explicit criterion for the positive definiteness of a general quartic form,” IEEE Trans. Automat. Contr., voL AC-10, pp. 372–373, July 1965
81. N. K. Bose and E. L Jury, “Inner algorithm to test for positive definiteness of arbitrary binary forms,” IEEE Trans. Automat. Contr., vol. AC-20, pp. 169–170, Feb. 1975
82. E. I. Jury, “The three p's in system theory,” in Proc. 1972 Int. Symp. Circuit Theory, pp. 32–37, Apr
83. ——, “Comments on ‘On the Routh-Hurwitz criterion’,” IEEE Trans. Automat. Contr. vol. AC-20, pp. 292–296, Apr. 1975
84. D. D. Åiljak, “Algebraic criteria for positive realness relative to the unit circle,” J. Franklin Inst., vol. 295, pp. 469–476, Apr. 1973
85. C. K. Sun and D. D. Åiljak, “Absolute stability test for discrete systems,” Electron. Lett., vol. 5, p. 236, May 1969
86. Y. Z. Tsypkin, “On the stability in the large of nonlinear sampled data systems,” Dokl. Akad. Nauk SSSR, vol. 145, pp. 52–55, 55, July 1962
87. E. I. Jury and B. W. Lee, “On the stability of a certain class of nonlinear sampled-data systems,” IEEE Trans. Automat. Contr., vol. AC-9, pp. 51–61, Jan. 1964
88. E. L Jury, The Theory and Application of the z-Transform Method. New York: Wiley, 1964, ch. 3
89. R. W. Newcomb, Linear Multiport Synthesis. New York: McGraw-Hill, 1966
90. B. D. O. Anderson and S. Vonpanitlerd, Network Analysis and Synthesis: A Modern System Approach. Englewood Cliffs, N. J.: Prentice-Hall, 1973
91. E. L Jury and B. W. Lee, “A stability theory for multinonlinear control systems,” presented at the 3rd IFAC Congr., London, England, June 1966
92. K. S. Narendra and J. Taylor, Frequency Domain Criteria for Absolute Stability. New York: Academic Press, 1974
93. H. G. Ansell, “On certain two-variable generalizations of circuit theory, with applications to networks of transmission lines and lumped reactances,” IEEE Trans. Circuit Theory, vol. CT-11, pp. 214–223, June 1964
94. T. S. Huang, “Stability of two-dimensional recursive filters,” IEEE Trans. Audio Electroacoust., vol. AU-20, pp. 158–163, June 1972
95. B. D. O. Anderson and E. I. Jury, “Stability test for two-dimensional dimensional recursive filters,” IEEE Trans. Audio Electroacoust., vol. AU-21, pp. 366–372, Aug. 1973
96. —, “Stability of multidimensional digital filters,” IEEE Trans. Circuits and Systems, vol. CAS-21, pp. 300–304, Mar. 1974
97. N. K. Bose and E. I. Jury, “Positivity and stability tests for multidimensional filters (discrete-continuous),” IEEE Trans. Accoust. Speech, Signal Processing, vol. ASSP-22, pp. 174–180, June 1974
98. D. D. Åiljak, “Stability criteria for two-variable polynomials,” School of Eng., Univ. Santa Clara, Santa Clara, Calif., Rep. NGR 05-010-7401, June 1974
99. E. I. Jury and S. M. Ahn, “Interchangeability of inners and minors,” ASME J. Dynamics Syn., Measurement Contr., vol. 257, pp. 257–260, Dec. 1971
100. W. D. Fryer, “Applications of Routh's algorithm to network-theory theory problems,” IRE Trans. Circuit Theory, vol. CT-6, pp. 144–149, June 1959
101. H. M. James, N. B. Nichols, and R. J. Phillips, Theory of Servo-mechanisms. New York: McGraw-Hill, 1947, sec. 7.9
102. G. C. Newton, Jr., L. A. Gould, and J. F. Kaiser, Analytical Design of Linear Feedback Controls. New York: Wiley, 1957, app. E
103. E. P. Popov, The Dynamics of Automatic Control Systems. Reading, Mass.: Addison-Wesley, 1962, p. 367
104. A. H. Katz, “On the question of calculating the quadratic criterion for regulation,” Prikl. Mekh., vol. 16, p. 362, 1952
105. W. A. Mersman, “Evaluation of an integral occuring in servo-mechanism theory,” Pac. J. Math., vol. 2, pp. 627–632, 1952
106. E. I. Jury, and A. G. Dewey, “A general formulation of the total square integrals for continuous systems,” IEEE Trans. Automat. Contr., vol. AC-10, pp. 119–120, Jan. 1965
107. F. Schneider, “Geschlossene forneln zur berechnung der quadratischen und der zeit beschwerten quadratischen regelfläche für kontinuierliche und diskrete systems,” Regelungstechnik, vol. 14, p. 159, 1966
108. J. Lehoczky, “The determination of simple quadratic integrals by Routh coefficients,” Periodica Polytech, vol. 10, pp. 153–166, 166, 1966
109. J. Neklony and J. Benes, “Simultaneous control of stability and quality of adjustment,” in Proc. 1960 IFAC Congr. London, England: Butterworth, 1961, vol. 2, pp. 734–744
110. F. H. Effertz, “On two coupled matrix algorithms for the evaluation of the RMS error criterion of linear system,” Proc. IEEE, vol. 54, pp. 879–880, June 1966
111. K. J. Astrom, Introduction of Stochastic Control Theory. New York: Academic Press, 1970, vol. 70, pp. 116–142
112. A. T. Fuller, “The replacement of saturation constraints by energy constraints in control optimization theory,” Int. J. Contr., vol. 6, no. 3, pp. 201-207, 1967
113. R. E. Kalman and J. E. Bertram, “Control system analysis and design via the second method of Lyapunov, Part I,” Trans. June 1963
114. A. G. J. Macfarlane, “The calculation of functionals of the time and frequency response of a linear constant coefficient dynamical system,” Quart. J. Mech. Appl. Math., vol. 16, pp. 250–271, 1963
115. R. J. Beshara, “A new evaluation of the mean square integral,” Trans. ASME J. Dynamic Syst., Measurement Contr., pp. 242–246, 246, Dec. 1971
116. M. H. Hamza and M. E. Ramsey, “Evaluation of time weighted total-square integrals.” Electron. Lett., vol. 7, May 1971
117. E. L Jury, “A note on the evaluation of the total square integral,” IEEE Trans. Automat. Contr., vol. AC-10, pp. 110–111, Jan. 1965
118. P. LeFevre, Optimalisation, Statistique des Systemes Dynamiques. Paris, France: Dunod, 1965, pp. 103–115
119. C. J. Greaves, G. A. Gagne, and G. W. Bordner, “Evaluation of integrals appearing in minimization problems of discrete-data systems,” IEEE Trans. Automat. Contr., vol. AC-11, pp. 145–148, 148, Jan. 1966
120. K. J. Astrom, E. L Jury, and R. G. Agniel, “A numerical method for the evaluation of complex integrals,” IEEE Trans. Automat. Contr., vol. 468–471, Aug. 1970
121. W. Gersch, “Computation of the mean-square response of a stationary time-discrete system,” IEEE Trans. Automat. Contr., vol. AC-16, p. 277, June 1971
122. S. Gutman, “The ‘inners’ formulation for the total square integral (continuous and discrete time systems),” Dep. Mech. Eng., Univ. California, Berkeley, M. S. Project 72-Sp-147, June 1972
123. V. Strejc, Lecture Notes, Univ. Minnesota, Dec. 1970 (Visiting from Inst. Inform. Theory and Automation, Prague, Czechloslovakia)
124. F. T. Man, “Evaluation of time-weighted quadratic performance indices for linear discrete systems,” IEEE Trans. Automat. Contr., vol. AC-15, 496–497, Aug. 1970
125. M. F. Gardner and J. L. Barnes, Transients in Linear Systems, vol. 1. New York: Wiley, 1942
126. Y. Sawaragi and A. Fukaw, “On the sum of squares values of sampled-data,” Trans. Japan. SME, Part I, vol. 25, July 1959
127. V. Strejc, Teorie Linéari Regulace. Prague, Czechoslovakia: Fakultaelektrotechnika Ceske Vysoké uceni technicke V, 1968, pp. 109–118
128. F. Csaki and J. Lehoczky, “Comment on ‘A remark on Routh's array’,” IEEE Trans. Automat. Contr., vol. AC-12, pp. 462–463, 463, Aug. 1969
129. E. I. Jury and S. Gutman, “The inner formulation for the total square integral (SUM),“ Proc. IEEE, vol. 61, pp. 395–397, Mar. 1973
130. S. K. Mitra, K. Hirano, and H. Sakaguchi, “A simple method of computing the input quantization and multiplication roundoff errors in a digital filter,” IEEE Trans. Accoust. Speech, Signal Processing, vol. ASSP-22, pp. 326–329, Oct. 1974
131. E. I. Jury and A. G. Dewey, “Relationship between the total square integral formula and the stability determinants,” Univ. of California, Berkeley, ERL Tech. Rep. M-78, July 1964
132. A. G. J. Macfarlane, “Functional-Matrix theory for the general linear electrical network,” Proc. Inst. Elec. Eng., vol. 112, p. 763, Apr. 1965
133. S. Barnett, “Evaluation of discrete linear system performance indices using Kronecker products,” Int. J. Contr., vol. 20, no. 5, pp. 849–855, 1974
134. S. O. Rice, “Efficient evaluation of integrals of analytic functions by the trapezoidal rule,” Bell Syst. Tech. J., vol. 52, pp. 707–722, May-June 1973
135. E. I. Jury and S. Gutman, “On the time weighted quadratic sum of linear discrete systems,” to be published
136. S. K. Mitra and R. J. Sherwood, “Canonic realizations of digital filters using the continued fraction expansion,” IEEE Trans. Audio Electroacoust. vol. Au-20, 185–194, Aug. 1972
137. L. Weinberg, “Single variable synthesis of mixed lumped-distributed distributed networks,” in Proc. 1974 IEEE. Int. Symp. Circuits and Systems, pp. 81–90
138. S. N. Basuthakur, J. M. Milne, and J. K. San, “Some new results on a class of periodically varying systems,” Int. J. Electron., vol. 1973
139. R. E. Kalman, “On the general theory of control systems,” in Proc. 1st mt. Congr. IFAC, Automat. and Remote Control. London, England: Butterworth, 1961, pp. 481–492
140. H. H. Rosenbrock, “Some properties of relatively prime polynomials matrices,” Electron. Lett, vol. 4, July 26, 1969
141. E. I. Jury, “Inner algorithm test for controllability and observability,” IEEE Trans. Automat. Contr., vol. AC-18, pp. 682–683. Dec. 1973
142. E. L Jury and P. S. Kamat, “Inner algorithm test for extraction of controllable, observable parts,” IEEE Trans. Automat. Contr. vol. AC-19, p. 278–279, June 1974
143. S. H. Wang and E. J. Davison, “A new invertibility criterion for linear multivariable systems,” IEEE Trans. Automat. Contr., vol. AC-18, pp. 538–539, Oct. 1973
144. J. L. Massey and M. K. Sabi, “Inverses of linear sequential circuits,” IEEE Trans. Comput, vol. C-17, pp. 330–337, Apr. 1968
145. M. K. Sain and J. L. Massey, “Invertibility of linear time-invariant invariant dynamical system,” IEEE Trans. Automat. Contr., vol. AC-14, 141–149, 1969
146. L. M. Silverman, “Inversion of multivariable linear systems,” IEEE Trans. Automat. Contr., vol. AC-14, pp. 270–276, June 1969
147. ——, “Properties and applications of inverse systems,” IEEE Trans. Automat. Contr., vol. AC-13, pp. 436–437, Aug. 1968
148. S. P. Singh, “A note on inversion of linear systems,” IEEE Trans. Automat. Contr., voL AC-15, pp. 492–493, Aug. 1970
149. D. C. Youla and P. Dorato, “On the inverse of linear dynamical systems,” Polytech. Inst., Brooklyn, N. Y., Electrophys. Memo. PIBMRI-1319-66, Mar. 1966
150. R. W. Brockett, “Poles, zeros, and feedback: State space inter-pretation,” IEEE Trans. Automat. Contr., vol. AC-10, pp. 129–135, 135, Apr. 1965
151. R. W. Brockett and M. D. Mesarovic, “The reproducibility of multivariable systems,” J. Math. Anal. Appl., vol. 11, pp. 548–563, 563, July 1965
152. S. H. Wang, “Relationship between triangular decoupling and invertibility,” Int. J. Contr., vol. 15, pp. 395–399, Feb. 1972
153. E. L Jury, “On the invertibility of linear dynamic systems,” to be published
154. F. M. Brasch, Jr. and J. B. Pearson, “Pole placement using dynamic compensators,” IEEE Trans. Automat. Contr., vol. AC-15, pp. 34–43, Feb. 1970
155. H. S. Wall, Analytic Theory of Continued Fractions. New York: Van Nostrand, 1948, pp. 161–166
156. A. J. Berkhout, “On the minimum phase criterion of sampled signals,” IEEE Trans. Geosci. Electron., vol. GE-11, pp. 186–198, 198, Oct. 1973
157. M. Tinkham, Group Theory and Quantum Mechanics. New York: McGraw-Hill, 1964
158. G. W. King, R. M. Haines, and P. C. Cross, “The asymmetric rotors-I: Calculation and symmetry classification of energy levels,” J. Chem. Phys., vol. 11, pp. 27–42, Jan. 1973
159. S. C. Wang, “On the assymmetrical top in quantum mechanics,” Phys. Rev. 2nd set., vol. 34, pp. 243–252, July 15, 1929
160. R. P. Tewarson, “Computations in sparse matrices,” SIAM Rev., vol. 12, pp. 527–543, Oct. 1970
161. M. M. Adibi, P. M. Hirsch, and T. A. Jordan, Jr., “Solution methods for transient and dynamic stability,” Proc. IEEE, vol. 62, pp. 951–958, July 1974
162. E. L Jury, “Remarks on ‘the mechanics of bilinear transformation’,” IEEE Trans. Audio Electroacoust., vol. Au-21, pp. 380– 382, 382, Aug. 1973
163. I. G. Sarma and M. A. Pal, “A note on the Liapunov matrix equation for ‘Linear discrete systems,” IEEE Trans. Automat. Contr., voL AC-13, pp. 119–121, Feb. 1968
164. E. I. Jury and S. M. Ahn, “A computational algorithm for inners,” IEEE Trans. Automat Contr., vol. AC-17, pp. 541–543, Aug. 1972
165. P. S. Kamat, “On computational algorithms for inners,” IEEE Trans. Automat. Contr., AC-19, 154–155, 1974
166. C. Sturm, “Autres demonstrations du mime theoreme,” J. Math. Pure Appl., vol. 1, pp. 290–308, 1826
167. A. L. Cauchy, “Calcul des indices des fonctions,” J. École Polytech., vol. 15, pp. 176–230, 1837
168. E. I. Jury and B. D. O. Anderson, “Some remarks on simplified stability criteria for continuous linear systems,” IEEE Trans. Automat. Contr., vol. AC-17, pp. 371–372, June 1972
169. B. D. O. Anderson, “The reduced Hermite criterion with application to proof of Lienard-Chipart criterion,” IEEE Trans. Automat. Contr., vol. AC-17, pp. 669–672, Oct. 1972
170. S. Barnett, “Interchangeability of the Routh and Jury tabular algorithms for linear system zero location,” presented at IEEE Decision and Control Conf., San Diego, Calif., Dec. 1973
171. M. Böcher, Introduction to Higher Algebra. New York: Macmillan, 1907, chs. 15 and 16
172. R. E. Kalman, “On the Hermitan Fujiwara theorem in stability theory,” Quart. Appl. Math., 1965
173. E. B. Van Vleck, “On the determination of a series of Sturm's functions by the calculation of a single determinant,” Ann. Math., vol. 1, pp. 1–13, Oct. 1899
174. S. Barnett, “Matrices, polynomials, and linear time-invariant systems,” IEEE Trans. Automat. Contr., vol. AC-18, pp. 1–10, Feb. 1973
175. G. Szego, “Orthogonal polynomials,” Amer. Math. Soc., p. 377, 1967
176. B. D. 0. Anderson, “Hurwitz polynomiak, LC and RC positive real functions, and the Hermite matrix,” IEEE Trans. Circuit Theory, voL CT-19, pp. 495-496, Sept. 1972
177. E. I. Jury and S. M. Ahn, “On orthogonal polynomials,” to be published