Stability Analysis And Estimation Of The Domain Of Attraction Of Impulsive Systems Subject To Input Saturation

Instantaneous phenomena are widespread in ecosystems,economic systems,physical systems,and many other areas.Impulsive systems,as a kind of suitable mathematical,deeply describe and characterize such phenomena.On the other hand,saturation is ubiquitous in engineering applications.Due to the physical constraints,the magnitude of the signal that an actuator or sensor can transmit is limited.If saturation nonlinearity is ignored or not treated appropriately in the design of the controller,then some undesirable behaviors may be encountered.The research on the stability of impulsive systems subject to input saturation has become a hot topic in academia.This paper mainly discusses the stability analysis and estimation of the domain of attraction of nonlinear impulsive systems subject to input saturation.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.In Chapter 2,for nonlinear impulsive systems with continuous input saturation,we investigate the exponential stability of such systems in the framework of input saturation,where two kinds of impulse effects,i.e.,impulsive control and impulsive disturbance,are considered,respectively.Some conditions based on Lyapunov stability theory are obtained for local exponential stability and stabilizability(LES)of the considered system.We present an optimization algorithm to design the controller and enlarge the estimation of the domain of attraction.Finally,two examples are given to illustrate the effectiveness of the theoretical research method.In Chapter 3,the problem of LES of nonlinear impulsive systems is studied,where saturation structure of impulse action is fully considered.Based on impulsive control theory and average dwell time(ADT)technique,sufficient conditions for LES are derived.To get a less conservative estimate of the domain of attraction,a linear matrix inequality(LMI)based algorithm is proposed to solve such kind of optimization problems.In chapter 4,for nonlinear time-delay impulsive systems subject to input saturation,both time-delay impulsive control problem and time-delay impulsive disturbance problem are considered to investigate locally uniformly exponential stability(LUES)of the systems.Moreover,the design problem of the controller in order to obtain a maximized estimation of the domain of attraction is formulated via a convex optimization problem.Two examples are presented to illustrate the sharpness of the main results.