Stability And H_∞ Analysis Of Discrete Switched System With Time Delay

With technical development, people gradually realize that there are many switching phenomena in real industrial systems. Such as the transmission system of automobile, air conditioning switch control system, large power grid control system. The performance we need for the industrial system is getting better and better. Selecting the appropriate switched system can bring better performance, which is what we hope to see. Due to the different subsystems, the stability of the switched system becomes more and complex. Over years, many scholars have carried out a lot of analysis on the switched system and give an amount of meaningful switched system stability criteria. In this paper, considering discrete time del ay switched systems, we get a new stability criterion. On the above, the paper analyzes the H∞ performance of the discrete time-delay switched systems and deduce LMI conditions to suit the H∞ performance. The main contents of this paper are as follows.Starting from discrete systems with time delay, this paper analyzes the stability of the system in a new perspective. All of the matrixes of the Lyapunov-Krasovskii function are not required to be positive definite. A new delay dependent stability criterion is given in the form of linear matrix inequality. This result is extended to the switched systems with time delay and a new result of the stability of discrete-time switched systems with time delay is obtained. Further, with the above research, we get the sufficient conditions for robust H∞ performance.For a class of discrete-time switched systems with interval time-varying delay, the method of dividing the time delay is used. And the upper and lower bound of time delay is used to propose a new class of Lyapunov function. The forward subtraction of Lyapunov function is estimated by Jensen summation inequality and inverse convex combination technique. Using this function the stability criterion of time delay discrete switched systems is obtained. On this basis, analyze the H∞ performance of the system. And give the conditions to meet the of H∞ performance.