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Global stabilization of composite stochastic systems. (English) Zbl 0876.60036

Summary: The aim of this paper is to investigate the stabilizability problem for composite stochastic systems and to apply the results to partially linear composite stochastic systems. In particular, we state sufficient conditions under which there exists a feedback law which renders the equilibrium solution of the closed-loop system deduced from a composite stochastic system exponentially stable in mean square. In the case of partially linear composite stochastic systems, the stabilizing feedback law is linear and is related to the solution of a stochastic Riccati-type equation.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
93E15 Stochastic stability in control theory
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References:

[1] Byrnes, C. I.; Isidori, A., New results and examples in nonlinear feedback stabilization, Systems and Control Letters, 12, 437-442 (1989) · Zbl 0684.93059
[2] Kokotovic, P. V.; Sussmann, H. J., A positive real condition for global stabilization of nonlinear systems, Systems and Control Letters, 13, 125-133 (1989) · Zbl 0684.93066
[3] Sontag, E. D., Smooth stabilization implies coprime factorization, IEEE Transactions on Automatic and Control, 34, 435-443 (1989) · Zbl 0682.93045
[4] Tsinias, J., Sufficient Lyapunov-like conditions for stabilization, Mathematics of Control Signals and Systems, 2, 343-357 (1989) · Zbl 0688.93048
[5] Lin, Z.; Saberi, A., Semi-global stabilization of partially linear composite systems via linear dynamic state feedback, (Proceedings of the \(32^{nd}\) IEEE CDC. Proceedings of the \(32^{nd}\) IEEE CDC, San Antonio, TX (1993)), 2538-2543 · Zbl 1375.82077
[6] Saberi, A.; Kokotovic, P. V.; Sussmann, H. J., Global stabilization of partially linear composite systems, SIAM Journal of Control and Optimization, 28, 6, 1491-1503 (1990) · Zbl 0719.93071
[7] Chabour, R.; Florchinger, P., Exponential mean square stability of partially linear stochastic systems, Appl. Math. Lett., 6, 6, 91-95 (1993) · Zbl 0797.93044
[8] Khasminskii, R. Z., Stochastic Stability of Differential Equations (1980), Sijthoff & Noordhoff: Sijthoff & Noordhoff Alphen aan den Rijn · Zbl 1259.60058
[9] Arnold, L., Stochastic Differential Equations: Theory and Applications (1974), Wiley: Wiley New York · Zbl 0278.60039
[10] Gao, Z. Y.; Ahmed, N. U., Feedback stabilizability of nonlinear stochastic systems with state-dependent noise, International Journal of Control, 45, 2, 729-737 (1987) · Zbl 0618.93068
[11] Florchinger, P., Lyapunov-like techniques for stochastic stability, SIAM Journal of Control and Optimization, 33, 4, 1151-1169 (1995) · Zbl 0845.93085
[12] P. Florchinger, Feedback stabilization of affine in the control stochastic differential systems by the control Lyapunov function method, SIAM Journal of Control and Optimization (to appear).; P. Florchinger, Feedback stabilization of affine in the control stochastic differential systems by the control Lyapunov function method, SIAM Journal of Control and Optimization (to appear). · Zbl 0874.93092
[13] Kushner, H. J., Converse theorems for stochastic Liapunov functions, SIAM Journal of Control and Optimization, 5, 2, 228-233 (1967) · Zbl 0183.19401
[14] Wonham, W. M., On a matrix Riccati equation of stochastic control, SIAM Journal of Control and Optimization, 6, 4, 681-697 (1968697) · Zbl 0182.20803
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