Partial Lévy Stabilization Of Time-varying Delayed Discrete Markovian Jump Linear Systems

In this paper,the first problem we discuss is the partial Lévy stabilization of time-delayed discrete Markovian jump linear systems.By the classifiy of markov chain,the time-delayed discrete Markovian jump linear system is divided into two parts that one is observable part and the other is objectivity part.By adopting stochastic analysis tools and linear matrix inequalities(LMIs),the stabilition controller of the observable part is designed to stabilize by Lévy noise.By using Shur lemma,the theorem is extended.We obtian a more practical theorem by taking advantage of the properties of the matrix and weaken theorem conditions,then we use Shur lemma to generalize the theorems.The second problem we disscuss in this paper is the partial Lévy stabilization of neutral time-delayed discrete Markovian jump linear systems.Through change the Lyapunov functions which we used in the proof of the theorem that we get in problem one,use the similar methods,we get two stabilization theorems and two corollaries.This article is elaborated as follow:The first chapter is the introduction part.The first section in this chapter give the research background,research significance,research contents and innovation points;in the second section,we show the necessary notation statement in this article.The second chapter,we discuss the partial Lévy stabilization of time-delayed discrete Markovian jump linear systems.In the first section,we give the systems model which need to be stabilized.The second section,Lévy noise is added to this model,use a markov chain to classify the system state,by observable part,using the Lévy noise,give the hypothes which need to stabilize this model,realize the stabilization of time-delayed discrete Markovian jump linear systems,give the stabilization theorem,this is one of the main conclusion of this paper.With the help of the Lyapunov function and matrix related knowledges,acquire the proof of the theorem,through Shur lemma,get more practical corollaries and by weakening theorem conditions,to simplify the theorem conditions,and then through Shur lemma,get the corollary of the theorem.The third chapter discuss the partial Lévy stabilization of neutral time-delayed discrete Markovian jump linear systems.In the first section,by using the method which similar to the second chapter,give the model of neutral time-delayed discrete Markovian jump linear systems which added the Lévy noise.The second section give the hypothesis and lemma need to stabilize the model,and then give the stabilization theorem,this is the second main conclusion of this paper.By changing the Lyapunov functions which is used in the proved of theorem in second chapter,then use similar method,acquire the proof of the theorem.