A characterization of solutions of the discrete-time algebraic Riccati equation based on quadratic difference forms

Linear Algebra and Its Applications

Volumn 416, Issue 2-3, 2006, Pages 1060-1082

  Kojima, Chiaki ^a   Takaba, Kiyotsugu ^a   Kaneko, Osamu ^b   Rapisarda, Paolo ^c  

^a KYOTO UNIVERSITY   (Japan)

^b OSAKA UNIVERSITY   (Japan)

^c UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

Author keywords

Behavioral approach; Discrete timealgebraicRiccatiequation; Dissipativesystem; Quadraticdifferenceforms; Spectral factorization; Storage function

Indexed keywords

EQUATIONS OF STATE; FUNCTION EVALUATION; HAMILTONIANS; QUADRATIC PROGRAMMING; RICCATI EQUATIONS; STATE SPACE METHODS;

BEHAVIORAL APPROACH; DISCRETE TIME ALGEBRAIC RICCATI EQUATION; DISSIPATIVE SYSTEM; QUADRATIC DIFFERENCE FORMS; SPECTRAL FACTORIZATION; STORAGE FUNCTION;

MATRIX ALGEBRA;

EID: 33646922102     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2005.11.027     Document Type: Article

References (20)

1. Willems J.C. Least squares stationary optimal control and the algebraic Riccati equation. IEEE Trans. Automat. Contr. AC-16 6 (1971) 621-634
2. Willems J.C. On the existence of a non-positive solution to the Riccati equation. IEEE Trans. Automat. Contr. AC-19 5 (1974) 592-593
3. Molinari B.P. Conditions for non-positive solutions of the linear matrix inequality. IEEE Trans. Automat. Contr. AC-20 6 (1975) 804-806
4. Trentelman H.L. When does the algebraic Riccati equation have a negative semidefinite solution?. In: Blondel V., Sontag E., Vidyasager M., and Willems J. (Eds). Open Problems in Mathematical Systems and Control Theory (1998), Springer-Verlag, New York 229-237
5. Trentelman H.L., and Rapisarda P. Pick matrix conditions for sign-definite solutions of the algebraic Riccati equation. SIAM J. Contr. Optim. 40 3 (2001) 969-991
6. Clements D.J., and Wimmer H.K. Existence and uniqueness of unmixed solutions of the discrete-time algebraic Riccati equation. Syst. Contr. Lett. 50 5 (2003) 343-346
7. Trentelman H.L., and Willems J.C. Every storage function is a state function. Syst. Contr. Lett. 32 5 (1997) 249-259
8. Kaneko O., and Fujii T. When is a storage function a state function in discrete time?. SIAM J. Contr. Optim. 42 4 (2003) 1374-1394
9. Pappas T., Laub A.J., and Sandell J.N.R. On the numerical solution of the discrete-time algebraic Riccati equation. IEEE Trans. Automat. Contr. AC-25 4 (1980) 631-641
10. Katayama T. A spectral factorization algorithm for discrete-time descriptor systems via generalized eigenproblems. Linear Algebra Appl. 205-206 (1994) 869-891
11. Stewart G.W. Introduction to Matrix Computations (1973), Academic Press, New York
12. Van Dooren P. A generalized eigenvalue approach for solving Riccati equations. SIAM J. Sci. Statist. Comput. 2 2 (1981) 121-135
13. Willems J.C. Paradigms and puzzles in the theory of dynamical systems. IEEE Trans. Automat. Contr. AC-36 11 (1991) 259-294
14. Rapisarda P., and Willems J.C. State maps for linear systems. SIAM J. Contr. Optim. 35 3 (1997) 1053-1091
15. Willems J.C., and Trentelman H.L. On quadratic differential forms. SIAM J. Contr. Optim. 36 5 (1998) 1703-1749
16. Kaneko O., and Fujii T. Discrete time average positivity and spectral factorization in a behavioral framework. Syst. Contr. Lett. 39 1 (2000) 31-44
17. Hoffman J., and Prätzel-Wolters D. Dipolynomial minimal bases and linear systems in AR representation. Linear Algebra Appl. 205-206 (1994) 777-803
18. Popov V. Hyperstability of Control Systems (1973), Springer Verlag, Berlin
19. Kailath T. Linear Systems (1980), Prentice-Hall, Eaglewood Cliffs, NJ
20. Polderman J.W., and Willems J.C. Introduction to Mathematical Systems Theory: A Behavioral Approach (1998), Springer-Verlag, New York