Mean square exponential stability for some stochastic linear discrete time systems

European Journal of Control

Volumn 12, Issue 4, 2006, Pages 373-395

  Dragan, Vasile ^a   Morozan, Toader ^a  

^a INSTITUTE OF MATHEMATICS   (Romania)

Author keywords

Discrete time linear stochastic systems; Independent random perturbations; Lyapunov operators; Markov chains; Mean square exponential stability

Indexed keywords

CHAINS; CONTINUOUS TIME SYSTEMS; DIGITAL CONTROL SYSTEMS; DISCRETE TIME CONTROL SYSTEMS; LYAPUNOV FUNCTIONS; MARKOV PROCESSES; SPACE FLIGHT; STOCHASTIC CONTROL SYSTEMS; SYSTEM STABILITY;

DISCRETE TIME; DISCRETE-TIME LINEAR STOCHASTIC SYSTEM; INDEPENDENT RANDOM PERTURBATION; LINEAR POSITIVE OPERATORS; LINEAR STOCHASTIC SYSTEM; LYAPUNOV OPERATOR; MARKOVIAN JUMPING; MEAN-SQUARE EXPONENTIAL STABILITIES; QUADRATIC LYAPUNOV FUNCTION; RANDOM PERTURBATIONS;

STOCHASTIC SYSTEMS;

EID: 39049136813     PISSN: 09473580     EISSN: None     Source Type: Journal    
DOI: 10.3166/ejc.12.373-395     Document Type: Article

References (29)

1. El Bouhtouri A, Hinrichsen D, Pritchard AJ. H1 type control for discrete-time stochastic systems. Int J Robust Nonlinear Control 1999; 9: 923-948
2. Costa OLV, Fragoso MD. Necessary and sufficient conditions for mean square stability of discrete-time linear systems subject to Markovian jumps. In: Proceedings 9-th Int. Symp. on Math. Theory of Networks and Systems 1991; Kobe, Japan, pp. 85-86
3. Costa OLV, Fragoso MD. Stability results for discrete time linear systems with Markovian jumpingpara-meters. J Math Anal Appl 1993; 179(2): pp.154-178
4. Costa OLV, Marques RP. Mixed H2=H1 Control of discrete time Markovian jump linear systems. IEEE Trans Autom Control 1998; AC-43(1): 95-100
5. Costa OLV, Fragoso MD, Marques RP. Discrete-time Markov jump linear systems. Springer Verlag London Limited 2005
6. Curtain RF. Stability of Stochastic Dynamical Systems. Lecture Notes in Mathematics, vol. 294. Springer Berlin HeidelbergNew-York, 1972
7. Damm T, Hinrichsen D. Newton's method for a rational matrix equation occuringin stochastic control. Linear Algebra Appl 2001; 332/334: 81-109
8. Da Prato G, Zabczyk J. Stochastic equations in infinite dimensions. Cambridge University Press, Cambridge, 1992
9. Doob JL. Stochastic processes. Wiley, New-York, 1967
10. Dragan V, Freiling G, Hochhaus A, Morozan T. A class of nonlinear differential equations on the space of symmetric matrices. Schriftenreihe des Instituts fur Mathematik SM-DU-561, 2003
11. Dragan V., Morozan T. Exponential stability for discrete time linear equations defined by positive operators. Integral Equ Oper Theory 2006; 54: 465-493. (Online first 2005 Birkhauser VerlagBasel/Switzer-land DOI 10.1007/s00020-005-1371-7, p. 1-29, http://dx.doi.org/10.1007/s00020-005-1371-7)
12. Fang Y., Loparo K. Stochastic stability of jump linear systems, IEEE Trans Autom Control 2002; 47(7): 1204-1208
13. Feng X, Loparo K. Stability of linear Markovian jump systems. In: Proc. 29-th IEEE Conf. Decision Control, 1408, Honolulu, Hawaii, 1990
14. Feng X, Loparo K, Ji Y, Chizeck HJ. Stochastic stability properties of jump linear systems. IEEE Trans. Autom Control 1992; 37(1): 38-53
15. Ji Y, Chizeck HJ, Feng X, Loparo K. Stability and control of discrete-time jump linear systems. Control Theory Adv Tech 1991; 7(2): 247-270
16. Khasminskii RZ. Stochastic Stability of Differential Equations. Sythoff and Noordhoff, Alpen aan den Ryn, 1980
17. Krtolica R, Ozguner U, Chan H, Goktas H, Winkelman J, Liubakka M. Stability of linear feedback systems with random communication delays. In: Proc. 1991 ACC, Boston, MA, June 26-28, 1991
18. Mariton M. Jump linear systems in automatic control. Marcel Dekker, New-York, 1990
19. Morozan T. Stability and control of some linear discrete-time systems with jump Markov disturbances. Rev. Roum. Math. Rures et Appl 1981; 26(1): 101-119
20. Morozan T. Optimal stationary control for dynamic systems with Markovian perturbations. Stochastic Anal Appl 1983; 1 (3): 299-325
21. Morozan T. Stability and control for linear discrete-time systems with Markov perturbations. Rev Roum Math Pures et Appl 1995; 40 (5-6): 471-494
22. Morozan T. Stabilization of some stochastic discrete time control systems. Stochastic Anal Appl 1983; 1 (1): 89-116
23. Morozan T. Stability radii of some discrete time systems with independent random perturbations. Stochastic Anal Appl 1997; 15 (3): 375-386
24. Morozan T. Dual linear quadratic problem for linear control systems with jump Markov perturbations. Rev Roum Math Pures et Appl 1996; 41 (5-6): 363-377
25. Ran ACM, Reurings MCB. The symmetric linear matrix equation. The Electronic Journal of Linear Algebra 2002; 9: 93-107
26. Wonham WH. Random Differential Equations in Control Theory. In Probabilistic Methods in Applied Mathematics; Barucha-Reid, A.T., Ed.; Academic Press: New York, 2, pp. 131-212, 1970
27. Yong J, Zhou XY. Stochastic Controls. Hamiltonian Systems and HJB Equations, Springer-Verlag, New York, 1999
28. Zabczyk J. An introduction in probability theory, Control Theory Topics Funct Analysis 1, IAEA, Vienna, pp. 419-462, 1976
29. Zabczyk J. Stochastic control of discrete-time systems. Control Theory Topics Funct Analysis 3, IAEA, Vienna, pp. 187-224, 1976