Mode-identifying time estimation and switching-delay tolerant control for switched systems: An elementary time unit approach

In this paper, an elementary time unit (ETU) method is proposed to study the problem of estimating the admissible delay in the identification of the active mode in the analysis and design of switched systems. The activation interval of a subsystem is considered to consist of a finite-time number of segments called ETUs, by which a novel class of time-scheduled Lyapunov function is used to estimate the admissible delay in mode identification for switched systems. Further, the ETU method is applied for switching-delay tolerant control problem, and a class of time-scheduled state feedback controllers are designed to achieve the exponentially stability. Several numerical examples are presented to validate the theoretic findings.