Robust Stability Analysis For Markov Jump System With Partly Unknown Transition Probabilities

The Markov jump system is a kind of random switching system with Markov jump.The switching between each of its subsystem follows the Markov process.It can be described the actual system with random jump of structure or parameter.In recent years,the study of the Markov jump system has attracted the attention of many scholars.The research results cover a number of areas,such as manufacturing system,flight control system,power system and even economic system etc.In this paper,the stability and robust control problems of Markov jump system with partly unknown transition probabilities are studied by constructing the suitable Lyapunov function,using Integral Inequalities,Linear Matrix Inequalities(LMI)and Schur complementary lemma.The main research results are as follows:1.The stability of the jump linear system is discussed.By using the properties of the rows' sum of the transition probability is zero in the continuous-time Markov jump system,the sufficient conditions for the stability of the LMI based Markov jump system are obtained.At the same time,a numerical example is given to verify the effectiveness of the method.2.The robust control problem of the jump linear system is discussed.By improving the stability analysis results of the existing literature,the sufficient conditions for the stability of the Markov jump system in continuous-time are obtained by using LMI and other methods,and the sufficient conditions for the system 2H and H? robust stabilization are given.A numerical example is given to verify that the given method has a little bit of conservatism.3.The robust stabilization problem of a class of uncertain Markov jump linear systems with partly unknown transition probabilities is studied.The sufficient conditions for robust stabilization of the Markov jump system are obtained and given in the form of LMI,and the given method does not need to know any information of the unknown transition probabilities,so that the result has a wider range of application.Finally,the numerical example is given to verify the effectiveness of the proposed method.4.The problem of stochastic stability of a kind of uncertain time-delay Markov jump system with partly unknown transition probabilities is studied.By constructing a suitable Lyapunov function based on the Lyapunov stability theory,estimating the upper bounds of the integral term with the free weight matrix and the convex combination method,and considering the relation between the upper and lower bounds of the time delay,a sufficient condition for stochastic stability of jump systems is given,and it is given in the form of LMI.Finally,a numerical example is given to illustrate the effectiveness of the proposed method.