Abstract
This paper is concerned with the finite-time stabilization of a class of switched nonlinear singular systems under asynchronous control. Asynchronism here refers to the delays in switching between the controller and the subsystem. First, the dynamic decomposition technique is used to prove that such a switched singular system is regular and impulse-free. Secondly, based on the state solutions of the closed-loop system in the matched time period and the mismatched time period of the system instead of constructing a Lyapunov function, the sufficient conditions for the finite-time stability of the asynchronous switched singular system are given, there is no limit to the stability of subsystems. Then, the mode-dependent state feedback controller that makes the original system stable is derived in the form of strict linear matrix inequalities. Finally, numerical examples are given to verify the feasibility and validity of the results.
Highlights
A switched system is a class of hybrid system consisting of several continuous or discrete dynamic subsystems and a given switching rule
When simulating complex models, switched systems often have an advantage over a single system, so they are widely used in many fields such as switching power converters, aircraft and air-traffic control, see [1,2,3,4,5]
The difference between the concept of finite-time stability and Lyapunov stability is mainly manifested in two aspects: one is that finite-time stability analyzes the system within a limited time interval; the other is that finite-time stability requires preset boundaries of system variables
Summary
A switched system is a class of hybrid system consisting of several continuous or discrete dynamic subsystems and a given switching rule. We are curious about one thing: can we solve the problem of finite-time stability of switched singular systems under asynchronous control without using the Lyapunov function method? Starting from the original solution of the system and combining the model with the mode-dependent average dwell time to study the asynchronous problem of a switched singular system has not been given enough attention, which is the second motivation of this paper. (iii) Based on the mathematical derivation and analysis of the state solution, and combined with the average dwell time method, the sufficient conditions for the FTS of the closed-loop switched singular system are obtained. Based on the decomposition transformation of the original system and taking the asynchronous controller into account, sufficient conditions for finite-time stability of switched singular systems are given. Matrix P > Q(P ≥ Q) is equivalent to P – Q > 0(P – Q ≥ 0). λmax(P)(λmin(P)) denotes the maximum (minimum) eigenvalue of P, and · is the Euclidean norm
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