A new approach to detectability of discrete-time infinite Markov jump linear systems

SIAM Journal on Control and Optimization

Volumn 43, Issue 6, 2005, Pages 2132-2156

  Costa, Eduardo F ^a   Do Val, João B R ^b   Fragoso, Marcelo D ^c  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

^b UNIVERSITY OF CAMPINAS   (Brazil)

^c LABORATÓRIO NACIONAL DE COMPUTAÇÃO CIENTÍFICA   (Brazil)

Author keywords

Detectability; Infinite Markov state space; Markov jump systems; Optimal control; Stochastic systems

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; INVARIANCE; LINEAR CONTROL SYSTEMS; MARKOV PROCESSES; OPTIMAL CONTROL SYSTEMS; QUADRATIC PROGRAMMING; STATE SPACE METHODS;

DETECTABILITY; INFINITE MARKOV STATE SPACE; MARKOV JUMP SYSTEMS; OPTIMAL CONTROL; STOCHASTIC SYSTEMS;

DISCRETE TIME CONTROL SYSTEMS;

EID: 27844504230     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S036301290342992X     Document Type: Article

References (17)

1. E. F. COSTA AND J. B. R. DO VAL, On the detectability and observability of discrete-time Markov jump linear systems, Systems Control Lett., 44 (2001), pp. 135-145.
2. E. F. COSTA AND J. B. R. DO VAL, On the detectability and observability of continuous-time Markov jump linear systems, SIAM J. Control Optim., 41 (2002), pp. 1295-1314.
3. E. F. COSTA AND J. B. R. DO VAL, Weak detectability and the linear quadratic control problem of discrete-time Markov jump linear systems, Int. J. Control, 16/17 (2002), pp. 1282-1292.
4. E. F. COSTA, J. B. R. DO VAL, AND M. D. FRAGOSO, On a detectability concept of discrete-time infinite Markov jump linear systems, Stochastic Analysis and Applications, to appear.
5. E. F. COSTA, J. B. R. DO VAL, AND M. D. FRAGOSO, On a detectability concept of discrete-time infinite Markov jump linear systems, in Proceedings of the 15th Triennal World Congress IFAC, 2002, pp. 2660-2665.
6. O. L. V. COSTA, Discrete-time coupled Riccati equations for systems with Markov switching parameters, J. Math. Anal. Appl., 194 (1995), pp. 197-216.
7. O. L. V. COSTA AND M. D. FRAGOSO, Discrete-time LQ-optimal control problems for infinite Markov jump parameter systems, IEEE Trans. Automat. Control, 40 (1995), pp. 2076-2088.
8. M. D. FRAGOSO AND J. BACZYNSKI, Optimal control for continuous time problems with infinite Markov jump parameters, SIAM J. Control Optim., 40 (2001), pp. 270-297.
9. M. D. FRAGOSO AND J. BACZYNSKI, Lyapunov coupled equations for continuous-time infinite Markov jump linear systems, J. Math. Anal. Appl., 274 (2002), pp. 319-335.
10. M. D. FRAGOSO AND J. BACZYNSKI, Stochastic versus mean square stability in continuous time linear infinite Markov jump parameter systems, Stochastic Anal. Appl., 20 (2002), pp. 347-356.
11. Y. JI AND H. J. CHIZECK, Controllability, stabilizability and continuous time Markovian jump linear quadratic control, IEEE Trans. Automat. Control, 35 (1990), pp. 777-788.
12. T. MOROZAN, Stability and control for linear systems with jump Markov perturbations, Stochastic Anal. Appl., 13 (1995), pp. 91-110.
13. W. S. GRAY AND J. P. MESKO, Observability functions for linear and nonlinear systems, Systems Control Lett., 38 (1999), pp. 99-113.
14. R. A. HORN AND C. R. JOHNSON, Matrix Analysis, Cambridge University Press, Cambridge, UK, 1990.
15. T. KAILATH, Linear Systems, Prentice-Hall, Englewood Cliffs, NJ, 1980.
16. K. KNOPP, Infinite Sequences and Series, Dover, New York, 1956.
17. I. R. PETERSEN, Notions of observability for uncertain linear systems with structured uncertainty, SIAM J. Control Optim., 41 (2002), pp. 345-361.