J-inner-outer factorization, J-spectral factorization, and robust control for nonlinear systems

IEEE Transactions on Automatic Control

Volumn 41, Issue 3, 1996, Pages 379-392

  Ball, Joseph A ^a,b   Van Der Schaft, Arjan J ^a,c  

^a IEEE

^b VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

^c UNIVERSITY OF TWENTE   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; CHEMICAL PLANTS; CONTROL SYSTEM SYNTHESIS; DIFFERENTIAL EQUATIONS; INTEGRATION; MATRIX ALGEBRA; OPTIMAL CONTROL SYSTEMS; PROCESS CONTROL; ROBUSTNESS (CONTROL SYSTEMS); STATE SPACE METHODS; SYSTEM STABILITY;

CHEMICAL PROCESS CONTROL; HAMILTON-JACOBI EQUATION; J-INNER-OUTER FACTORIZATION; J-SPECTRAL FACTORIZATION;

NONLINEAR CONTROL SYSTEMS;

EID: 0030104565     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.486639     Document Type: Article

References (36)

1. V. I. Arnold, Mathematical Methods of Classical Mechanics, 2nd ed. Berlin: Springer-Verlag, 1989.
2. J. A. Ball and J. W. Helton, "Shift invariant manifolds and nonlinear analytic function theory," Integral Equations Operator Theory, vol. 11, pp. 615-725, 1988.
3. _, "Factorization and general properties of nonlinear Toeplitz operators," in The Gohberg Anniversary Collection, vol. II, H. Dym, S. Goldberg, M. A. Kaashoek, and P. Lancaster. Eds. Basel: Birkhauser-Verlag, 1989, pp. 25-41.
4. _, "Inner-outer factorization of nonlinear operators," J. Functional Anal., vol. 104, pp. 363-413, 1992.
5. ∞ control theory for stable plants," Math. Contr., Signals Syst., vol. 5, pp. 233-261, 1992.
6. ∞-control and J-inner-outer factorization," submitted for publication.
7. J. A. Ball, J. W. Helton, and M. Verma, "A factorization principle for stabilization of linear control systems," Int. J. Robust Nonlinear Contr., vol. 1, pp. 229-294, 1991.
8. ∞-control for nonlinear systems with output feedback," IEEE Trans. Automat. Contr., vol. 38, pp. 546-559, 1993.
9. J. A. Ball and M. Verma, "Factorization and feedback stabilization for nonlinear systems," Syst. Contr. Lett., vol. 23, pp. 187-196, 1991.
10. H. Bart, I. Gohberg, and M. A. Kaashoek, Minimal Factorization of Matrix and Operator Functions. Basel: Birkhauser-Verlag, 1979.
11. ∞-Optimal Control and Related Minimax Design Problems: A Dynamic Game Approach. Basel: Birkhauser-Verlag, 1991.
12. P. E. Crouch and A. J. van der Schaft, Variational and Hamiltonian Control Systems. Basel: Springer-Verlag, 1987.
13. F. J. Doyle, F. Allgoewer, and M. Morari, "A normal form approach to approximate input-output linearization for maximum phase nonlinear systems," IEEE Trans. Automat. Contr., to appear.
14. ∞-controller synthesis by J-lossless coprime factorizations," SIAM J. Contr. Opt., vol. 30, pp. 522-547, 1992.
15. ∞-control," SIAM J. Contr. Opt., vol. 28, pp. 1350-1371, 1990.
16. ∞ control via measurement feedback," J. Math. Syst., Estimation Contr., vol. 2, pp. 31-35.
17. ∞-control via measurement feedback in nonlinear systems," IEEE Trans. Automat. Contr., vol. 37, pp. 1283-1293, 1992.
18. ∞ control," J. Math. Syst., Estimation, Contr., vol. 4, pp. 401-450, 1994.
19. ∞ optimal controllers," Syst. Contr. Lett., vol. 13, pp. 205-210, 1989.
20. ∞ control of nonlinear systems: A class of controller," California Institute of Technology, Tech. Memo 93-008, 1993.
21. ∞ control," Int. J. Robust Nonlinear Contr., vol. 1, pp. 47-68, 1991.
22. ∞ control," Syst. Contr. Lett., vol. 16, pp. 1-8, 1991.
23. ∞ control," IEEE Trans. Automat. Contr., vol. 37, pp. 770-784, 1992.
24. ∞ control theory," in Essays on Control: Perspectives in the Theory and its Applications, H. L. Trentelman and J. C. Willems, Eds. Basel: Birkhauser-Verlag, 1993, pp. 153-190.
25. A. J. van der Schaft and J. A. Ball, "Inner-outer factorization of nonlinear state space systems," in Systems and Networks: Mathematical Theory and Applicatons, vol. II, U. Helmke, R. Mennicken, and J. Sauer, Eds. Berlin: Akademie Verlag, 1994, pp. 53-56.
26. _, "Nonlinear inner-outer factorization," in Proc. 33rd Conf. Decision Contr., Lake Buena Vista, FL, 1994, pp. 2549-2552.
27. _, in preparation.
28. M. Vidyasagar, Nonlinear Systems Analysis. San Diego: Prentice-Hall, 1993.
29. J. C. Willems, "Dissipative dynamical systems, Part I: General theory," Arch. Rat. Mech. Anal., vol. 45, pp. 321-351, 1972.
30. R. A. Wright and C. Kravaris, "Nonminimum-phase compensation for nonlinear processes," AIChE J., vol. 38, pp. 26-40, 1992.
31. M. Berger, Nonlinearity and Functional Analysis: Lectures on Nonlinear Problems in Functional Analysis. New York: Academic, 1977.
32. D. J. Hill and P. J. Moylan, "Connections between finite gain and asymptotic stability," IEEE Trans. Automat. Contr., vol. 25, pp. 931-936, 1980.
33. 2-gain bounded uncertainty," Syst. Contr. Lett., vol. 24, pp. 75-81, 1995.
34. M. Vidyasagar and A. Vannelli, "New relationships between input-output and Lyapunov stability," IEEE Trans. Automat. Contr., vol. 27, pp. 481-483, 1982.
35. J. L. Wyatt, L. O. Chua, J. W. Gannett, I. C. Goknar, and D. N. Green, "Energy concepts in the state-space theory of nonlinear n-ports: Part II - Losslessness," IEEE Trans. Circuits Syst., vol. 29, pp. 417-430, 1982.
36. J. W. Helton and M. R. James, "An information approach to nonlinear J-inner-outer factorization," in Proc. 33rd Conf. Decision Contr., Lake Buena Vista, FL, 1994, pp. 2565-2571.