Abstract
For affine switched systems, the existence of multiple equilibria is related to subsystems owing to the affine terms, which makes asymptotic and finite-time stability analysis nontrivial. In this paper, the problems of finite-time boundedness (FTB) analysis and stabilization are addressed for affine switched systems, and several definitions and sufficient conditions are proposed to study FTB and H∞ performance. At first, the definition of FTB for affine switched systems is improved concerning the affine terms and multiple equilibria. Based on the FTB definition, sufficient conditions ensuring finite-time boundedness for affine switched systems under a prespecified state boundary are given. Then the results are extended to solve H∞ finite-time boundedness problem, in which the H∞ controllers are designed to guarantee the finite-time boundedness of affine switched system with H∞ performance. In our investigation, average dwell-time approach is employed to study the time-dependent constrained switching case. Finally, several numerical examples are given to illustrate the effectiveness of the proposed results.
Highlights
Switched systems are distinctive subclass of hybrid systems
Finding sufficient conditions ensuring the Lyapunov asymptotic stability dealing with infinite time interval has been the major concern for switched systems
The theory of finite-time stability (FTS) and finite-time boundedness (FTB) focuses on the transient response of dynamical systems over a finite-time interval, while asymptotic behavior is for infinite time
Summary
Switched systems are distinctive subclass of hybrid systems. They are composed of a family of continuous-time or discrete-time subsystems with a criterion that rules the switching among them. The theory of finite-time stability (FTS) and finite-time boundedness (FTB) focuses on the transient response of dynamical systems over a finite-time interval, while asymptotic behavior is for infinite time. The main objective in this paper is to find sufficient conditions ensuring the FTB of affine switched systems by switching signal and feedback controllers design and to drive the state of affine switched system to the prescribed neighborhood of a desired equilibrium during a finite-time interval. Taking into account the influence of affine terms on FTB for affine switched system, we propose an innovative FTB concept Based on this definition, sufficient conditions ensuring the affine switched system finite-time bounded are proposed. Classifying subsystems into asymptotically stable and unstable systems, we get the less conservative results of finite-time boundedness for affine switched system with the help of additional information of switching signal.
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