Global exponential stability and [formula omitted] control of limit cycle for switched affine systems under time-dependent switching signal

Abstract

In this paper, the stability analysis of continuous-time switched affine systems (CTSASs) is addressed via dwell time switching. The main purpose of this note is to design a time-dependent switching signal assuring the global exponential stability of a desire limit cycle (which is selected from a set of attainable limit cycles). By constructing a discretized Lyapunov function and using the linear matrix inequalities technique, a set of conditions in the framework of dwell time are designed. For CTSASs, the performance indexes of the system in this neighborhood cannot be analyzed because most of the proposed controllers drive the system trajectory into a small enough neighborhood. Differently, the technique proposed in this note leads the CTSAS’s trajectory to the limit cycle so that the resulting conditions can consider the weighted H∞ performance level of the system. More specifically, the design conditions can be applied to open-loop subsystems that are unstable. At last, a numerical example and a practical example are given to illustrate our method.