Switched Dynamic Systems with Logic Switching and Its Stability Analysis
Tao Sun, Xudong Zhao, Xi‐Ming Sun
Abstract
In this paper, the stability problem for a class of switched dynamic systems with logic switching signals is investigated. Emphasis is placed on the stability of logically switched dynamic systems (LSDSs) derived by using logic and switching rules. First, the so-called LSDSs giving a further extension of switched dynamic systems is designed for the first time, which is formulated in a hybrid form of a switched dynamic system and a logical dynamic system. Second, the concept of global uniform exponential stability is extended to the one for the LSDSs. It is illustrated that some traditional concepts of stability can be seen as special cases of the extended stability. Third, through the mode-dependent average dwell time (MDADT), average cycle dwell time (ACDT), stable cyclic sequence dependent average cycle dwell time (S-ACDT), and unstable cyclic sequence dependent average cycle dwell time (U-ACDT), the stability problem for LSDSs with all stable or partly stable subsystems is solved. In other words, based on multiple Lyapunov functions and a digital transformation approach, the stability criteria for LSDSs containing all stable subsystems or partially unstable subsystems are obtained in the nonlinear case. Correspondingly, the stability conditions for LSDSs are also derived in the linear case. Finally, two examples are presented to demonstrate the feasibility of the established results.