Hybrid Systems with Time-Dependent Switching

Abstract

This chapter considers a broad class of HS whose switchings are activated according to time functions, i.e., a switching occurs at a certain time instant. These switching instants can be prescribed a priori and fixed, or designed arbitrarily by engineers. The motivation of researching HS appears from many practical systems e.g., circuit system, and also the switching control ideas. In this chapter, several FTC methods are presented for such HS. Two natural ideas follow: One way is to design FTC law in each faulty mode such that it is stable (Lyapunov stable, asymptotical stable or input-to-state stable) or the output regulation problem of each mode is solvable, then apply the standard stability results on HS (see sections 2.1-2.3). Another way is to research directly the stability of HS without reconfiguring the controller in each unstable mode (see sections 2.4-2.5). These two ideas will be developed in this chapter. The switching control techniques as developed in Chapter 6 also have their roots in this chapter.