On the observability and detectability of linear stochastic systems with Markov jumps and multiplicative noise

Journal of Systems Science and Complexity

Volumn 23, Issue 1, 2010, Pages 102-115

  Ni, Yuanhua ^a   Zhang, Weihai ^b   Fang, Haitao ^a  

^a INSTITUTE OF SYSTEMS SCIENCE   (China)

^b SHANDONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

Exact detectability; Exact observability; Markov jump systems; Multiplicative noise; PBH Criterion; stochastic H 2 H control

Indexed keywords

DETECTABILITY; EXACT OBSERVABILITY; LINEAR STOCHASTIC SYSTEM; MARKOV JUMP SYSTEM; MULTIPLICATIVE NOISE;

PHASE NOISE; STOCHASTIC CONTROL SYSTEMS; STOCHASTIC SYSTEMS;

OBSERVABILITY;

EID: 77249174765     PISSN: 10096124     EISSN: 15597067     Source Type: Journal    
DOI: 10.1007/s11424-010-9270-7     Document Type: Article

References (24)

1. R. Z. Has'minskii, Stochastic Stability of Differential Equations, Sijtjoff and Noordhoff, Alphen, 1980.
2. R. S. Liptser and A. N. Shiryayev, Statistics of Random Processes, Springer-Verlag, New York, 1977.
3. J. M. Yong and X. Y. Zhou, Stochastic Controls: Hamiltonian Systems and HJB Equations, Springer, New York, 1999.
4. ∞ control in the presence of stochastic uncertainty, Int. J. Contr., 1998, 71: 219-237.
5. L. Arnold, Stochastic Differential Equations: Theory and Applications, John Wiley, 1974.
6. 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., 2005, 41: 1295-1314.
7. ∞ control for stochastic systems with Markovian jumps, Automatica, 2008, 44: 857-863.
8. M. Mariton, Jump Linear Systems in Automatic Control, Marcel Dekker, New York, 1990.
9. V. Dragan and T. Morozan, Stability and robust stabilization to linear stochastic systems described by differential equations with Markovian jumping and multiplicative white noise, Stoch. Anal. Appl., 2002, 20(1): 33-92.
10. P. Caines and J. F. Zhang, On the adaptive control of jump parameter systems via nonlinear filtering, SIAM J. Control Optim., 1995, 33: 1758-1777.
11. X. Mao, G. G. Yin, and C. Yuan, Stabilization and destabilization of hybrid systems of stochastic differential equations, Automatica, 2007, 43: 264-273.
12. L. Li and V. A. Ugrinovskii, On necessary and sufficient conditions for H-infinity output feedback control of Markov jump linear systems, IEEE Transactions on Automatic Control, 2007, 52(7): 1287-1292.
13. X. Li, X. Y. Zhou, and M. A. Rami, Indefinite stochastic linear quadratic control with Markovian jumps in infinite time horizon, Journal of Global Optimization, 2003, 27: 149-175.
14. T. Damm, On detectability of stochastic systems, Automatica, 2007, 43: 928-933.
15. G. Guatteri and F. Masiero, Infinite horizon and ergodic optimal quadratic control for an affine equation with stochastic coefficients, SIAM J. Control Optim., 2009, 48(3): 1600-1631.
16. W. Zhang and B. S. Chen, On stabilizability and exact observability of stochastic systems with their applications, Automatica, 2004, 40: 87-94.
17. W. Zhang, H. Zhang, and B. S. Chen, Generalized Lyapunov Equation Approach to State-Dependent Stochastic Stabilization/Detectability Criterion, IEEE Trans. Automat. Contr., 2008, 53: 1630-1642.
18. S. He, J. Wang, and J. Yan, Semimartingale and Stochastic Analysis, Science Press and CRC Press Inc, 1995.
19. L. E. Ghaoui and M. A. Rami, Robust state-feedback stabilization of jump linear systems via LMIs, International Journal of Robust and Nonlinear Control, 1996, 6: 1015-1022.
20. V. M. Ungureanu, Stochastic uniform observability of linear differential equations with multiplicative noise, J. Math. Anal. Appl., 2008, 343: 446-463.
21. T. Damm, Rational Matrix Equations in Stochastic Control, Lecture notes in Control and Information Sciences, Berlin-Heidelberg, Springer, 2004, Vol. 297.
22. J. W. Brewer, Kronecker products and matrix calculus in system theory, IEEE Trans. Circuits Syst., 1978, 25: 772-781.
23. B. D. O. Anderson and J. B. Moore, Optimal Control: Linear Quadratic Methods, Prentice Hall, Englewood Cliffs, New Jersey, 1989.
24. ∞ control with state-dependent noise, IEEE Trans. Automat. Contr., 2004, 49: 45-57.