In this paper, the stability properties for a class of switched stochastic systems with commutative componentwise subsystem matrices are studied. Under some switching law, the trivial solutions of the above systems ar...In this paper, the stability properties for a class of switched stochastic systems with commutative componentwise subsystem matrices are studied. Under some switching law, the trivial solutions of the above systems are proved to be exponentially stable in mean square and almost sure exponentially stable if the random perturbations are sufficiently “small”.展开更多
Sufficient conditions for the exponential stability of a class of nonlinear, non-autonomous stochastic differential equations in infinite dimensions are studied. The analysis consists of introducing a suitable approxi...Sufficient conditions for the exponential stability of a class of nonlinear, non-autonomous stochastic differential equations in infinite dimensions are studied. The analysis consists of introducing a suitable approximating solution systems and usig a limiting argument to pass on stability of strong solutions to mild ones. Consequently, under these conditions the random attractors of given stochastic systems are reduced to zero with exponential decay. Lastly, two examples are investigated to illustrate the theory.展开更多
This paper considers the problem of delay-dependent exponential stability in mean square for stochastic systems with polytopic-type uncertainties and time-varying delay. Applying the descriptor model transformation an...This paper considers the problem of delay-dependent exponential stability in mean square for stochastic systems with polytopic-type uncertainties and time-varying delay. Applying the descriptor model transformation and introducing free weighting matrices, a new type of Lyapunov-Krasovskii functional is constructed based on linear matrix inequalities （LMIs）, and some new delay-dependent criteria are obtained. These criteria include the delay-independent/rate- dependent and delay-dependent/rate-independent exponential stability criteria. These new criteria are less conservative than existing ones. Numerical examples demonstrate that these new criteria are effective and are an improvement over existing ones.展开更多
The robust exponential stability in mean square for a class of linearstochastic uncertain control systems is dealt with. For the uncertain stochastic systems, we havedesigned an optimal controller which guarantees the...The robust exponential stability in mean square for a class of linearstochastic uncertain control systems is dealt with. For the uncertain stochastic systems, we havedesigned an optimal controller which guarantees the exponential stability of the system. Actually,we employed Lyapunov function approach and the stochastic algebraic Riccati equation (SARE) to haveshown the robustness of the linear quadratic(LQ) optimal control law. And the algebraic criteria forthe exponential stability on the linear stochastic uncertain closed-loop systems are given.展开更多
基金Supported by the National Natural Science Foundation of China under Grant 10461001.
文摘In this paper, the stability properties for a class of switched stochastic systems with commutative componentwise subsystem matrices are studied. Under some switching law, the trivial solutions of the above systems are proved to be exponentially stable in mean square and almost sure exponentially stable if the random perturbations are sufficiently “small”.
文摘Sufficient conditions for the exponential stability of a class of nonlinear, non-autonomous stochastic differential equations in infinite dimensions are studied. The analysis consists of introducing a suitable approximating solution systems and usig a limiting argument to pass on stability of strong solutions to mild ones. Consequently, under these conditions the random attractors of given stochastic systems are reduced to zero with exponential decay. Lastly, two examples are investigated to illustrate the theory.
基金supported by the National Natural Science Foundation of China (No.60525303, 60604004, 60704009) Natural Science Foundationof Hebei Province, China (No.F2005000390, F2006000270)
文摘This paper considers the problem of delay-dependent exponential stability in mean square for stochastic systems with polytopic-type uncertainties and time-varying delay. Applying the descriptor model transformation and introducing free weighting matrices, a new type of Lyapunov-Krasovskii functional is constructed based on linear matrix inequalities （LMIs）, and some new delay-dependent criteria are obtained. These criteria include the delay-independent/rate- dependent and delay-dependent/rate-independent exponential stability criteria. These new criteria are less conservative than existing ones. Numerical examples demonstrate that these new criteria are effective and are an improvement over existing ones.
文摘The robust exponential stability in mean square for a class of linearstochastic uncertain control systems is dealt with. For the uncertain stochastic systems, we havedesigned an optimal controller which guarantees the exponential stability of the system. Actually,we employed Lyapunov function approach and the stochastic algebraic Riccati equation (SARE) to haveshown the robustness of the linear quadratic(LQ) optimal control law. And the algebraic criteria forthe exponential stability on the linear stochastic uncertain closed-loop systems are given.
