Finite Time Stability Of Switched System With Time Delay

Switching system is typical dynamic hybrid systems, which contains several subsystems and a switching rate, switching rate depends on each moment subsystems. In recent years,switched systems Lyapunov stability and robust stability has been a rapid progress in detail, it has wide application background, such as intelligent conversion system, robot control systems,chemical process control systems and power systems.The theory of linear parameter-varing control systems gives a new method for the gain design of system, its industrialization to the process control in the field of aerospace has a wide range of applications. Comprehensive conditions of linear dynamic system parameter can use a single lyapunov function to transform into a optimization problem of linear matrix inequality(lmi), and they can also be a secondary or depend on the parameter of the problem, and even the whole parameter space. The switched systems, with linear parameter-varing dynamic system contacted closely, can be described by using the interaction of continuous time system and discrete system, it usually depends on the state and the dual function of time. This kind stability analysis of switched dynamic system is a very important and challenging major issues, it has received extensive attention of the experts and scholars in the recent literature.In addition, many researchers pay attention to the control theory to a practical problem, in general, the stability is based on the sense of lyapunov under the condition of infinite time interval. However, it is not possible in real life, so finite-time stability in finite-time interval caused the great attention naturally of experts and scholars, and then it is further explored. We will explored the state of the system in finite time interval is or not bounded for the following two types of dynamic system, i. e. the finite time stability.(i) Finite-time stability of impulse switched system without parameter.We seek a sufficient condition using the tools of lyapunov function and inequality for three different systems: continuous impulse switching systems with nonlinear impulse, continuous nonlinear impulse switching systems with time delay, continuous nonlinear impulse switching systems with nonlinear time delay, without parameter, in finite time interval. We also have given a strict proof. Finally, the simulation is given to verify the validity of conclusion.(ii) Finite-time stability of linear switched system with parameter.Under the condition of depending on a parameter, conbined with the existing literature,linear switched delay systems are explored what guarantee its path does not exceed the adequacy of the threshold condition in finite time interval using the method of the linear matrix inequality and the average dwell time, conbining with the relative inequality lemma. In other words, the sufficient conditions are just the finite-time stability.