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Abstract
This paper is concerned with a state observer-based sliding mode control design methodology for a class of continuous-time state-delayed switched systems with unmeasurable states and nonlinear uncertainties. The advantages of the proposed scheme mainly lie in which it eliminates the need for state variables to be full accessible and parameter uncertainties to be satisfied with the matching condition. Firstly, a state observer is constructed, and a sliding surface is designed. By matrix transformation techniques, combined with Lyapunov function and sliding surface function, a sufficient condition is given to ensure asymptotic stability of the overall closed-loop systems composed of the observer dynamics and the estimation error dynamics. Then, reachability of sliding surface is investigated. At last, an illustrative numerical example is presented to prove feasibility of the proposed approaches.
Highlights
A switched system consists of a finite number of subsystems described by a class of differential or difference equations and a logical law that is used to orchestrate switching between these subsystems [1]
As the paper [19, 20] improved, this paper presents a new observer design for a class of uncertain nonlinear state-delayed switched systems by using the sliding mode control theory
The motivation of our work is to introduce an sliding mode control (SMC) scheme based on observer for a class of switched systems that are uncertain nonlinear state-delayed systems with unmeasurable state, unknown nonlinear function, and mismatching parameter uncertainties
Summary
A switched system consists of a finite number of subsystems described by a class of differential or difference equations and a logical law that is used to orchestrate switching between these subsystems [1]. In Wu’s work [19] a new robust stability condition based on observer is proposed for a class of uncertain nonlinear neutral delay systems by using the sliding mode control theory combined with reaching law technique. The motivation of our work is to introduce an SMC scheme based on observer for a class of switched systems that are uncertain nonlinear state-delayed systems with unmeasurable state, unknown nonlinear function, and mismatching parameter uncertainties. This is a new Mathematical Problems in Engineering problem in SMC and switched systems research areas. An example is given to prove the feasibility of the proposed approaches
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