Resilient Control And Filtering Of Stochastic Time-delay Systems

Stochastic perturbations and time delay are frequently encountered in many practicaldynamic systems. These systems can’t be described by ordinary differential equations, andthey should be modeled by using stochastic differential equation with delay. Recently,analysis and control for stochastic systems have been attached considerable attention.This paper focuses on resilient control and filtering of stochastic time-delay systems, andthe main contents are as follows:1. Finite-time output feedback resilient control is investigated for a class of stochastictime-delay system. Firstly, according to the resilient controller, the closed-loop augmentedsystem is presented. Then, using the Lyapunov function method and It lemma, finite-timestability of the closed-loop augmented system is obtained. Based on the finite-time stabilitycondition, a feedback controller is designed to ensure the stochastic finite-time stability of theclosed-loop system. Finally, the validity of the result is demonstrated by a numerical example.2. Resilient adaptive control for a class of stochastic time-delay systems is considered.The following three cases are handled: nonlinear perturbation and controller gain perturbationare both known; the former is known while the latter is unknown; and the former is unknownwhile the latter is known. By choosing appropriate Lyapunov function, resilient adaptivecontrollers for the above-mentioned three systems are developed, such that the resultingclosed-loop systems are stochastically asymptotically stable. Some errors in the literaturehave been corrected by constructing a new Lyapunov function. The effectiveness of themethod is illustrative by a numerical example.3. This paper is also concerned with the problem of resilient H filtering for stochastictime-delay systems. First of all, via the Lyapunov function method, H performancecriterion of the filtering error system is proposed. Then, resilient H filter is established. Anumerical example is provided to show the effectiveness of the result.Finally, the concluding remarks and future works are addressed in the end of the paper.