H-Representation and applications to generalized lyapunov equations and linear stochastic systems

IEEE Transactions on Automatic Control

Volumn 57, Issue 12, 2012, Pages 3009-3022

  Zhang, Weihai ^a   Chen, Bor Sen ^b  

^a SHANDONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b NATIONAL TSING HUA UNIVERSITY   (Taiwan)

Author keywords

Complete observability; generalized D stability and stabilization; generalized Lyapunov equations; H representation; weak stability and stabilization

Indexed keywords

COMPLETE OBSERVABILITY; D STABILITY; H-REPRESENTATION; LYAPUNOV EQUATION; WEAK STABILITY;

LYAPUNOV FUNCTIONS; MATHEMATICAL TECHNIQUES; OBSERVABILITY; STOCHASTIC SYSTEMS;

STABILIZATION;

EID: 84870415078     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2012.2197074     Document Type: Article

References (38)

1. B. D. O. Anderson and J. B. Moore, Optimal Control-Linear Quadratic Methods. Upper Saddle River, NJ: Prentice-Hall, 1990.
2. M. A. Rami and X. Y. Zhou, "Linear matrix inequalities, Riccati equations, and indefinite stochastic linear quadratic control, " IEEE Trans. Autom. Control, vol. 45, no. 6, pp. 1131-1142, Jun., 2000.
3. A. El Bouhtouri, D. Hinrichsen, and A. J. Pritchard, "Type control for discrete-time stochastic systems, " Int. J. Robust Nonlin. Control, vol. 9, pp. 923-948, 1999. (Pubitemid 30509398)
4. R. Bellman, Introduction to Matrix Analysis. Philadelphia, PA: SIAM, 1995.
5. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM, 1994.
6. V. Balakrishnan and L. Vandenberghe, "Semidefinite programming duality and linear time-invariant systems, " IEEE Trans. Autom. Control, vol. 48, no. 1, pp. 30-41, Jan. 2003.
7. W. L. Brogan, Modern Control Theory, 3rd ed. Upper Saddle River, NJ: Prentice-Hall, 1991.
8. B. S. Chen and W. Zhang, "Stochastic control with state-dependent noise, " IEEE Trans. Autom. Control, vol. 49, no. 1, pp. 45-57, Jan. 2004.
9. M. Chilali, P. Gahinet, and P. Apkarian, "Robust pole placement in LMI regions, " IEEE Trans. Autom. Control, vol. 44, no. 12, pp. 2257-2269, Dec. 1999.
10. M. Chilali and P. Gahinet, " design with pole placement constraints: An LMI approach, " IEEE Trans. Autom. Control, vol. 41, pp. 358-367, 1996. (Pubitemid 126767888)
11. E. F. Costa and J. B. R. do Val, "On the observability and detectability of continuous-time Markov jump linear systems, " SIAM J. Control Optim., vol. 41, pp. 1295-1314, 2002.
12. G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions. Cambridge, MA: Cambridge Univ. Press, 1992.
13. V. Dragan and T. Morozan, "Stochastic observability and applications, " IMA J. Math. Control Inf., vol. 21, pp. 323-344, 2004.
14. T. Damm, "On detectability of stochastic systems, " Automatica, vol. 43, pp. 928-933, 2007. (Pubitemid 46509772)
15. M. D. Fragoso, O. L. V. Costa, and C. E. de Souza, "A new approach to linearly perturbed Riccati equations arising in stochastic control, " Appl. Math. Optim., vol. 37, pp. 99-126, 1998. (Pubitemid 128684261)
16. Y. Feng and B. D. O. Anderson, "An iterative algorithm to solve state-perturbed stochastic algebraic Riccati equations in LQ zero-sum games, " Syst. Control Lett., vol. 59, pp. 50-56, 2010.
17. J. Feng, S. Xu, and W. Zhang, " output feedback control with spectrumconstraints for uncertain stochastic systems, " Circuits Syst. Signal Process., vol. 26, pp. 193-214, 2007. (Pubitemid 47161733)
18. S. Gutman and E. I. Jury, "A general theory for matrix root-clustering in subregions of the complex plane, " IEEE Trans. Autom. Control, vol. AC-, no. 4, pp. 853-863, Aug. 1981. (Pubitemid 12447457)
19. D. Hinrichsen and A. J. Pritchard, "Stochastic, " SIAM J. Control Optim., vol. 36, pp. 1504-1538, 1998.
20. R. Z. Has'minskii, Stochastic Stability of Differential Equations. Alphen aan den Rijn, The Netherlands: Sijtjoff and Noordhoff, 1980.
21. C. S. Kubrusly and O. L. V. Costa, "Mean square stability conditions for discrete stochastic bilinear systems, " IEEE Trans. Autom. Control, vol. AC-30, pp. 1082-1087, 1985. (Pubitemid 16524710)
22. R. E. Kalman, "On the general theory of control systems, " in Proc. IFAC First Int. Conf., Moscow, USSR, 1960, pp. 481-493.
23. Z. Y. Li, Y. Wang, B. Zhou, and G. R. Duan, "On unified concepts of detectability and observability for continuous-time stochastic systems, " Appl. Math. Comput., vol. 217, pp. 521-536, 2010.
24. Y. Liu, "Backward Stochastic Differential Equation and Stochastic Control System, " Ph. D. dissertation, Shandong Univ., China, 1999.
25. H. Mukaidani, "Soft-constrained stochastic Nash games for weakly coupled large-scale systems, " Automatica, vol. 45, pp. 1272-1279, 2009.
26. A. G. Mazko, "The Lyapunov matrix equation for a certain class of region bounded by algebraic curves, " Sov. Autom. Control, vol. 42, pp. 12-17, 1980.
27. J. M. Ortega, Matrix Theory. New York: Plenum, 1987.
28. I. R. Petersen, "Notions of observability for uncertain linear systems with structured uncertainty, " SIAM J. Control Optim., vol. 41, pp. 345-361, 2002.
29. R. Penrose, "A generalized inverse of matrices, " Proc. Cambridge Philos. Soc., vol. 52, pp. 17-19, 1955.
30. W. J. Rugh, Linear SystemTheory. Upper Saddle River, NJ: Prentice-Hall, 1993.
31. V. A. Ugrinovskii, "Observability of linear stochastic uncertain systems, " IEEE Trans. Autom. Control, vol. 48, no. 12, pp. 2264-2269, Dec. 2003.
32. J. L. Willems and J. C. Willems, "Feedback stabilizability for stochastic systems with state and control dependent noise, " Automatica, vol. 12, pp. 277-283, 1976.
33. Z. Wang, "Robust state estimation for perturbed systems with error variance and circular pole constraints: The discrete-time case, " Int. J. Control, vol. 73, pp. 303-311, 2000. (Pubitemid 35395441)
34. F. Yang, Z. Wang, Y. S. Hung, and H. Shu, "Mixed filtering for uncertain systems with regional pole assignment, " IEEE Trans. Aerosp. Electron. Syst., vol. 41, no. 2, pp. 438-448, Apr. 2005.
35. W. Zhang, H. Zhang, and B. S. Chen, "Generalized Lyapunov equation approach to state-dependent stochastic stabilization/detectability criterion, " IEEE Trans. Autom. Control, vol. 53, no. 7, pp. 1630-1642, Jul. 2008.
36. W. Zhang, Y. Huang, and L. Xie, "Infinite horizon stochastic control for discrete-time systems with state and disturbance dependent noise, " Automatica, vol. 44, pp. 2306-2316, 2008.
37. W. Zhang and L. Xie, "Interval stability and stabilization of linear stochastic systems, " IEEE Trans. Autom. Control, vol. 54, no. 4, pp. 810-815, Apr. 2009.
38. W. Zhang and B. S. Chen, "On stabilization and exact observability of stochastic systems with their applications, " Automatica, vol. 40, pp. 87-94, 2004.