The Finite-time Reliable Analysis For Stochastic Systems

Modern control systems are developing towards large and more complicated scale. If system failures occur in this kind of control systems, vast loss of lives and wealth is caused. It is important to improve reliability and safety of systems. Fault-tolerant control pioneers a new way to enhance the reliability of complicated systems. Moreover, much attention of many scholars has been devoted to the problem of finite-time stability and finite-time boundedness, and made a lot of theoretical results. Therefore, the research for finite-time robust fault-tolerant control with Markovian jump systems has important theoretical and practical significance.Based on the above discussion, in this paper, several types of the stochastic Markovian jump systems modulation are studied. In the meantime, several types of finite-time fault tolerant control for uncertain singular Markovian jump systems with bounded transition probabilities is discussed. To solve the different types of finite-time stability problems, the feasibility problem is translated into the optimization problem. At present, the stability of stochastic Markovian jump systems including robust stability,exponential stability and global asymptotic stability, etc. In addition, the finite-time stability problems of stochastic Markovian jump systems also attract the attention of many scholars, and made a lot of theoretical results.In this paper, the research of the reliable finite-time stability and boundedness of the stochastic Markovian jump systems is discussed by constructing the proper Lyapunov-Krasovskii functional, by applying weak infinitesimal generator, linear matrix inequality, liberty weight matrix and decoupling method. The main researches are as follows:First of all, the problem of reliable finite-time H_∞filtering for discrete time-varying delay systems with Markovian jump and randomly occurring nonlinearities was analyzed and discussed. The filtering error dynamic system is constructed based on an H_∞filter,by constructing a new Lyapunov function, using the theory of weak infinitesimal generator,sufficient criteria are provided to guarantee that the resulting filtering error system is stochastic finite-time boundedness and stochastic finite-time H_∞filtering in both normaland fault cases. simulation examples show the feasibility and effectiveness of the design method.Secondly, the problem of finite-time stabilization for one family of uncertain singular Markovian jump with bounded transition probabilities and nonlinearities systems was addressed. Sufficient criteria are provided such that the augmented system is singular stochastic finite-time boundedness and singular stochastic H_∞finite-time boundedness.Although the derived results are not in LMIs form, we can turn it into LMIs feasibility problem by employing a decoupling technique and fixing some parameters. Transformed into LMI feasibility problem. A numerical example to verify the effectiveness of the algorithm is given.Finally, the problem of reliable finite-time H_∞control is addressed for one family of uncertain singular nonlinear Markovian jump systems with time-varying delay subject to partial information on the transition probabilities. By using Lyapunov-Krasovskii functional theory, infinitesimal generator and decoupling technology, Sufficient criteria are provided such that the augmented system is singular stochastic finite-time boundedness and singular stochastic H_∞finite-time boundedness. A numerical of examples are given to show the validity of the proposed approach.