Stabilization and the Design of Switching Laws of a Class of Switched Singularly Perturbed Systems via the Composite Control

Chun-Tang Chao,Ding-Horng Chen,Juing-Shian Chiou

doi:10.3390/math9141664

Chun-Tang Chao, Ding-Horng Chen + Show 1 more

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https://doi.org/10.3390/math9141664

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Abstract

This paper proves that the controller design for switched singularly perturbed systems can be synthesized from the controllers of individual slow–fast subsystems. Under the switching rules of individual slow–fast subsystems, switched singularly perturbed systems can be stabilized under a small value of ε. The switching rule is designed on the basis of state transformation of the individual subsystems.

Highlights

The switched system is an example of a hybrid system
Switched systems represent a combination of many continuous or discrete systems such that the systems have a special switching law, and in accordance with this switching rule, the system switches to each subsystem operation
Using the composite state-feedback control method, the stabilization problem is is preUsing the composite state-feedback control method, the stabilization problem presented for a class of switched singularly perturbed systems in this paper

Summary

Introduction

The switched system is an example of a hybrid system. Switched systems represent a combination of many continuous or discrete systems such that the systems have a special switching law, and in accordance with this switching rule, the system switches to each subsystem operation. By using a novel quasi-time-dependent approach, they developed a stability analysis criterion for nonlinear switched systems. The Lyapunov stability theorem and genetic algorithm were employed to develop a stabilization and switching law design for switched discrete-time systems [8]. In view of the state-driven switching law, sufficient stability conditions with delay dependence were derived for switched time-delay systems [10]. Dragan considered a stochastic optimal control problem modeled using a system of singularly perturbed Itô differential equations with two fast time scales and derived the asymptotic structure of the stabilizing solution [17]. Liu et al [18] investigated the feedback control problem in a discrete-time singularly perturbed system under information constraints and employed the uniform quantization method. Lyapunov-function-based techniques are employed for the control of switched linear systems

Materials and Methods

Example

Conclusions