(A) study on stability analysis for hybrid switched systems

Abstract

Hybrid system is a new emerging area in control society. Since it can intrinsically comprise many different types of systems in its frame, the control technique for this area has been rapidly developed in recent years. A switched system occupies the one important portion of hybrid systems having a decision logic and continuous-time dynamical subsystems. In this dissertation, we study the stability analysis of hybrid switched systems. By introducing a redundancy factor as a basic analysis tool, we present the new methodology for analyzing the switching stability and establishing the switching law. Because the previous multiple Lyapunov function based stability analyses impose the restrictions not only on the behavior of individual Lyapunov functions being engaged so as to be monotonically non-increasing at all switching times but also on the switching law so as to have multiple appearance of the same engaged subsystems in associated switching sequence, they have some limitations for the cases where the constructed switching sequence has the form of only single engagement of each of subsystems up to infinite time, and the subsystems are locally stable under given attraction regions, and the some of subsystems are unstable. In this dissertation, we employ locally/globally decrescent functions, in stead of using multiple Lyapunov functions, described by exponential or class KL functions for each of subsystems in order to build a more practical stability criteria. The sufficient condition about switching stability has been built with the concept such that the state trajectory of engaged subsystem at switching instant ends up inside of the attraction region of next subsystem. The minimum (maximum) holding time for each subsystem is defined as the required time interval to preserve the stability at least (at most). The general switching stability is provided by means of introducing the redundancy factors for class KL functions. It extends and relaxes the scope o...