Stochastic observability and applications

IMA Journal of Mathematical Control and Information

Volumn 21, Issue 3, 2004, Pages 323-344

  Dragan, Vasile ^a   Morozan, Toader ^a  

^a INSTITUTE OF MATHEMATICS   (Romania)

Author keywords

Riccati differential equations; Stochastic observability; Stochastic stability; Stochastic systems

Indexed keywords

LINEAR CONTROL SYSTEMS; LINEAR EQUATIONS; LYAPUNOV METHODS; MARKOV PROCESSES; MATHEMATICAL OPERATORS; MATRIX ALGEBRA; OBSERVABILITY; RICCATI EQUATIONS; SYSTEM STABILITY; THEOREM PROVING; TIME VARYING CONTROL SYSTEMS; WHITE NOISE;

LINEAR DIFFERENTIAL EQUATION; MARKOVIAN JUMPING; STOCHASTIC OBSERVABILITY; STOCHASTIC STABILITY; TIME VARYING LINEAR SYSTEM;

STOCHASTIC CONTROL SYSTEMS;

EID: 3442898764     PISSN: 02650754     EISSN: None     Source Type: Journal    
DOI: 10.1093/imamci/21.3.323     Document Type: Article

References (20)

1. Anderson, B. D. O. & Moore, J. B. (1969) New results in linear system stability. SIAM J. Control, 7, 398-413.
2. Barbashin, M. A. & Krasovski, T. B. (1970) Introduction to the Theory of Stability (translated from the Russian edition Moskow 1967). Groningen: Volters-Noorthoff.
3. Bellman, R. (1970) Introduction to Matrix Analysis. New York: McGraw-Hill.
4. Brockett, J. B. (1979) Parametrically stochastic linear differential equations. Math. Program. Stud., 5, 8-12.
5. Doob, J. L. (1967) Stochastic Processes. New York: Wiley.
6. Dragan, V. & Morozan, T. (2003) Systems of matrix rational differential equations arising in connection with linear stochastic systems with Markovian jumping. J. Diff. Eqns, 194, 1-38.
7. Dragan, V. & Morozan, T. (2001) The linear quadratic optimization problem and tracking problem for a class of linear stochastic systems with multiplicative white noise and Markovian jumping. Preprint nr. 3/ 2001, Institute of Mathematics od Romanian Academy (to appear in IEEE Trans. Auto. Control).
8. Dragan, V. & Morozan, T. (2002) Stability and robust stabilization to linear stochastic systems described by differential equations with markovian jumping and multiplicative white noise. Stoch. Anal. Appl., 20, 33-92.
9. Friedman, A. (1975) Stochastic Differential Equations and Applications Vol. I. New York: Academic.
10. Haussmann, U. G. (1971) Optimal stationary control with state and control dependent noise. SIAM J. Control, 9, 184-198.
11. Ji, Y. & Chizeck, H. J. (1990) Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control. IEEE Trans. Automat. Control, 35, 777-788.
12. Kalman, R. (1960) Contributions on the theory of optimal control. Bul. Soc. Math. Mexicana (2), 5, 102-119.
13. Morozan, T. (1983) Optimal stationary control for dynamic systems with Markov perturbations. Stoch. Anal. Appl., 1, 299-325.
14. Morozan, T. (1993) Stochastic uniform observability and Riccati equations of stochastic control. Revue Roum. Math. Pures et Appl., 9, 771-781.
15. Morozan, T. (1995) Stability and control for linear system with jump Markov perturbation. Stoch. Anal. Appl., 13, 91-110.
16. Morozan, T. (2001) Linear quadratic control and tracking problems for time-varying stochastic differential systems perturbed by a Markov chain. Revue Roum. Math. Pure et Applique, 6, 783-804.
17. Oksendal, B. (2000) Stochastic Differential Equations 5th edn. Springer.
18. Zabczyk, J. (1975) On optimal stochastic control of discrete-time systems in Hilbert space. SIAM J. Control, 13, 1217-1234.
19. Wonham, W. H. (1968) On a matrix Riccati equation of stochastic control. SIAM J. Control Optim., 6, 312-326.
20. Wonham, W. H. (1970) Random diferential equations in control theory. Probabilistic Methods in Applied Mathematics, Vol. 2. (A. T. Barucha-Reid, ed.). New York: Academic, pp. 131-212.