Robust Fault Detection Of Markov Jump Systems With Partly Unknown Transition Probabilities

Markov jump systems are a class of special hybrid systems and used to describe the mutation of the external environment.With the continuous development of science and technology,industrial control systems become more and more complex,and the requirements for the reliability and security are getting higher,thus the research of robust fault detection for Markov jump systems is very necessary.In recent years,the main research achievements for Markov jump systems are obtained under the condition of completely known transition probabilities.However,the elements in transition probability matrices of Markov jump systems can't be completely obtained or the cost is probably very high in practical systems.Therefore,we research the problems of robust fault detection for Markov jump systems with partly unknown transition probabilities.The main contents of this paper are as follows:For discrete-time Markov jump systems with partly unknown transition probabilities,the problem of robust fault detection is investigated.At first,we construct the observer of the system and select the appropriate Lyapunov function.According to the obtained infinitesimal operator,the transition probabilities features of discrete-time jump systems and the free weighting matrix are introduced to separate the unknown parts of transition probabilities.Then,the sufficient conditions of progressive stability for robust fault detection observer are received and the corresponding design method of the observer is also given.Finally,optimizing the observer and completing the fault detection.For the singular Markov jump systems,we discuss the problem of robust fault detection with partly unknown transition probabilities and independent singular modal matrices.By combing the theory of Lyapunov stability with the definition of the regular and no pulse,we propose and prove the conditions for the stochastic admissibility of singular Markov jump systems.The LMI method is used to analyze the performance of the system,when the modal matrices of singular jump systems are independent.Furthermore,extending the method to the system of partly unknown transition probabilities.Finally,the optimal gain matrices of the observer are obtained by optimizing the robustness and sensitivity of the system.The problem of robust fault detection for nonlinear Markov jump systems with partly unknown transition probabilities is studied.The nonlinear Markov jump systems are linearized by using T-S fuzzy model.The obtained global fuzzy linear systems are constructed with the reconstructed observer.The interference signal and fault signal are represented with the corresponding residual signal.And the robustness to disturbances and the sensitivity of the fault signal are gotten.By using the characteristic of each line in transition probabilities for the continuous jump systems and LMI technology,the sufficient conditions for the stochastic stability and two performance indexes of the observer are given.The optimal gain matrices are gotten by optimizing iteration.