Stability And Stabilization Of A Class Of Markov Jump Random Time-delay Systems

Due to the randomness of the Markov jump system,the stochastic system with Markov jumps has a wide range of applications in modern engineering and science.The randomness of the random system with Markov jump is particularly widely used,so it is especially important for its theoretical research.Long time ago,many scholars and experts at home and abroad payed special attention to the study of such a random system,and also made some scientific research.In the last century,the birth of control theory and its extensive application in military,industrial and engineering fields have further promoted the development of Markov jump random system.Today,such system has become one of the current research hotspots.This paper studies one type of stability and stabilization problem with stochastic Markov jump time-delay system.First,the researching system is a random time-delay system with Markov jump in the derivative without delay information,it's stability and stabilization of the problem are studied in this paper by constructing a new LyapunovKrasovskii functional,a sufficient condition for the stability of such systems is obtained,and the stabilization of the system is further discussed.The design method of the time-delay state feedback controller of the closed-loop system is proposed.Secondly,we study the stability of neutral stochastic time-delay systems with Markov jumps.By using the Lyapunov stability theorem and the related inequality scaling techniques,we give sufficient condition of the stability of the system based on linear matrix inequality.In this paper,we study the mean square exponential stability of the systems.In this paper,the analytical methods used in the stability analysis of the systems are roughly the same.However,for the neutral stochastic time-delay systems with Markov jump,we need to add specific constraints to the differential operators in the system equation before using the Lyapunov-Krasovskii functional to get the discriminant condition of the mean square exponential stability.