Abstract
The mean square BIBO stability is investigated for stochastic control systems with mixed delays and nonlinear perturbations. The system with mixed delays is transformed, then a class of suitable Lyapunov functionals is selected, and some novel delay-dependent BIBO stabilization in mean square criteria for stochastic control systems with mixed delays and nonlinear perturbations are obtained by applying the technique of analyzing controller and the method of existing a positive definite solution to an auxiliary algebraic Riccati matrix equation. A numerical example is given to illustrate the validity of the main results.
Highlights
In recent years, Bounded-Input Bounded-Output BIBO stabilization has been investigated by many researchers in order to track out the reference input signal in real world, see 1–6 and some references therein
Motivated by the above discussions, the main aim of this paper is to study the BIBO stabilization in mean square for the stochastic control system with mixed delays and nonlinear perturbations
The nonlinear stochastic control system 2.1 or 3.1 with the control law 2.3 is BIBO stabilized in mean square if h1B1 < 1 and there exist symmetric positive-definite matrices Ri > 0, i 1, 2, . . . , 10, and Q1 > 0 such that λmin Q1 − 2α P > 0
Summary
In recent years, Bounded-Input Bounded-Output BIBO stabilization has been investigated by many researchers in order to track out the reference input signal in real world, see 1–6 and some references therein. Because of the finite switching speed, memory effects, and so on, time delays are unavoidable in technology and nature, commonly exist in various mechanical, chemical engineering, physical, biological, and economic systems. They can make the concerned control system be of poor performance and instable, which cause the hardware implementation of the control system to become difficult. In 14–16 , based on Riccati-equations, by constructing appropriate Lyapunov functions, some BIBO stabilization criteria for a class of delayed control systems with nonlinear perturbations were established. Based on the technique of analyzing controller and transforming of the system, various suitable Lyapunov functionals are selected, different Riccati matrix equations are established, and some sufficient conditions guaranteeing BIBO stabilization in mean square are obtained. A numerical example is provided to demonstrate the effectiveness of the derived results
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