Research On Input/Output-to-State Stability Of Hybrid Systems

With the development of society and science,the coupling of continuous dy-namic and discrete dynamic becomes more and more obvious in control process.Thus,the theoretical research of hybrid systems have gained popular attentions.Moreover,input(/output)-to-state stability provides an effective way to deal with the stability of forced systems.The research of input(/output)-to-state stability of hybrid systems becomes a hot topic in academia.This paper considers the input/output-to-state stability of hybrid systems.The main work of this paper is as follows:In Chapter 1,we introduce the background of our research,the main work of this paper,and some useful lemmas and definitions.In Chapter 2,we study the input/output-to-state stability of hybrid systems,where the impulsive switched system are mainly considered.Based on Lyapunov method and average dwcll-time method,a relationship between impulse signals,average dwell-time,and the increase or decay of the system is established.Two types of impulses,i.e.,sta-bilizing impulses and destabilizing impulses are fully considered.Some sufficient conditions which can ensure input/output-to-state stability of impulsive switched systems are proposed.Moreover,we consider the design of state-norm estimator of impulsive switched system.Finally,examples with its simulation are given to illustrate the effectiveness of our results.In Chapter 3,we study the input-to-state stability of hybrid systems via Lyapunov method involving indefinite derivative,where two types of systems,i.e.,impulsive systems and switched systems are con-sidered.Under this uncertain case,we propose some sufficient conditions which can ensure input-to-state stability of the systems based on Lyapunov method and average dwell-time method.Examples with its simulation are given to illustrate the validity of the proposed results.