Hybrid dynamical system is a class of nonlinear systems which contain both discrete variables and continuous variables, and the two kinds of variables interactive with each other. The stability of the system is an important component in both the control theory and the system project. As the stability of the system determines the possible using of the system in the project, so the research of the hybrid dynamical system has great meaning. This paper especially discusses the stability of two types of dynamic systems which are impulse system and impulsive switched system. The standards for system stability are get through the use of different methods such as Lyapunov method, Lie algebraic method, Razumikhii methods and different dealing techniques.For a class of parameter uncertainty impulsive system with multi-delay in the first chapter, we gave the delay-dependent asymptotic stability criterion. First by splitting the coefficient matrix, the system is converted into the system with discrete delay and distributed delay at the same time, then by constructing an operator, that is, constructing some novel Lyapunov-Krasovkii function, using this function, a various effective transforms, the theory of linear matrix inequalities, we can have a new non-delay dependent stability standard. In the proof of the gaved stability criterion, we not only use the theory of inequality and splitting the coefficient matrix, but also using the method of increasing the zero-entry skills, so the conclusion come which reduce the conservative nature and conducive to engineering using. The validity of the conclusions is explained by a numerical example.For a class of non-linear impulsive switched systems, first through the Lie algebra conditions determine its global exponential stability criterion. Examine the nature of all the subsystems coefficient matrices, based on this, divide this into two diffient situation, this is that all subsystem coefficient matrices are Hurwitz/Schur stability and not all of the subsystem coefficient matrices are Hurwitz/Schur stable to prove there must be a common Lyapunov function. By given a auxiliary function and the tacticy of designing dell time, the new global exponential stability criteria can be obtained. Then by constructing a Lyapunov function and using inequality analysis technique, conditions for the exponential stability of impulsive switched systems is given. |