Research On Input/output-to-state Stability Of Impulsive Switched Systems: Hybrid Impulses Effects

Generally speaking,the study on dynamics of impulsive systems can be di-vided into two classes:destabilizing impulses and stabilizing impulses.However,in reality,the impulses can have multiple actions,i.e.,systems are usually affected by the mixed effect of hybrid impulses.Considering that the impulses have double impacts on system behaviours,the research of impulsive switched systems involving hybrid impulses is very challenging and interesting.In addition,the external input often exists in real world,which may cause some bad performance of a system.As we know,the concept of input-to-state stability provides a powerful tool to char-acterize the effects of external inputs to a dynamical system.Thus the research of input-to-state stability of impulsive switched systems with hybrid impulses has become a hot topic in control theory area.This paper mainly studies the input(/output)-to-state stability of impulsive switched systems with hybrid impulses.The main works of this paper are as follows:In Chapter 1,we introduce the background of our research,the main works of this paper,and some useful definitions and lemmas.In Chapter 2,we study the Lyapunov stability and L₂-gain for impulsive switched systems,where two cases are considered:unstable subsystems with stabilizing impulses and stable subsystems with destabilizing impulses.Some sufficient conditions for exponential stability and L₂-gain of impulsive switched systems are proposed by using linear matrix inequal-ities.Based on average dwell time condition and Lyapunov method,a relationship among the average dwell time,impulses strength,and the decay or growth of sys-tem trajectories is established.Finally,two illustrative examples are given to show the effectiveness of the proposed results.In Chapter 3,we study the input/output-to-state stability of impulsive switched systems with delays,where the derivative of Lyapunov functions are assumed to be time-varying and mode-dependent.Based on the Lyapunov-Razumikhin method and the mode-dependent average dwell time condition,some Razumikhin-type criteria for input/output-to-state stability of im-pulsive switched systems with the coexistence of the destabilizing and stabilizing impulses are presented.Finally,two examples are provided to demonstrate the effectiveness of the proposed results.