Analysis And Synthesis Of Nonlinear Descriptor Semi-Markov Jump Systems

Many practical systems may have component failures,parameter changes,sudden changes in environmental conditions,abrupt changes in the operating point of nonlinear system,etc.,which cause unpredictable structural changes in the system.Note that the random abrupt changes can be described by the Markov process or chain.However,the sojourn time of Markov chain is exponentially distributed and its transition rate is constant,which is conserva-tive to a certain extent.Compared with Markov jump system,the transition rate function of semi-Markov jump system can not only follow exponential distribution,but also obey Weibull distribution and Gaussian distribution,or others.Due to its relaxed probability distribution,semi-Markov jump system has more extensive applications than Markov jump system,such as beam-cavity interaction system,reliability analysis,DNA analysis and so on.In this dissertation,we focus on the stochastic stability analysis,finite-time bound-edness analysis,finite-time filtering,T-S fuzzy control and resilient estimation of nonlinear descriptor semi-Markov jump system.This dissertation mainly include the following four chapters.Firstly,we introduce the research background and significance of semi-Markov jump system,and the current status of the descriptor nonlinear Markov jump system.Then,the introduction and current status of T-S fuzzy system is given,where the application of T-S fuzzy system to descriptor system and Markov jump system is mainly introduced.In the following,the current status of nonlinear descriptor system and descriptor Markov jump system is present-ed.In addition,the work and innovation of this dissertation are presented.In Chapter 2,the stability analysis and stabilization of nonlinear descrip-tor semi-Maxkov jump system are discussed.Firstly,a sufficient stochastic stability condition is obtained by using the stochastic Lyapunov functional and implicit function theorem.In order to give a solvable stochastic stabili-ty condition and design the state feedback controller for nonlinear descriptor semi-Markov jump system,the singular value decomposition of the differential matrix E is used to give another solvable stochastic stability condition.Fi-nally,the design method of the state feedback controller and the robust state feedback controller is proposed in terms of linear matrix inequality directly.In this chapter,no matrix inequality was introduced in the design of the con-troller,so the obtained results are less conservative than some existing ones.In the third Chapter,we study the finite-time boundedness analysis and stabilization of nonlinear descriptor semi-Markov jump system.Firstly,a suffi-cient condition is obtained by using the stochastic Lyapunov functional,which guarantees that the system is singular stochastic H? finite-time bounded.Then,in order to design the state feedback controller,by using the singular value decomposition of the differential matrix E,the singular stochastic H?finite-time boundedness of closed-loop system is obtained.Finally,a T-S fuzzy method is used to estimate the nonlinear descriptor semi-Markov jump system.By means of system augmentation and matrix inequality decoupling approach,we give a sufficient condition on singular stochastic H? finite-time bounded-ness of closed-loop system.In addition,the static output feedback controller of T-S fuzzy descriptor semi-Markov jump system is designed without any limits on freedom variables.In order to show the feasibility and practicability of the results,numerical examples are given at the end of this chapter.In Chapter 4,we study the issue of finite-time H? filter design for non-linear descriptor semi-Markov jump system.Firstly,by using the stochastic Lyapunov functional and implicit function theorem,sufficient conditions for the singular stochastic finite-time boundedness of the filtering error system axe given.Then,using the matrix decoupling technique and linear matrix in-equality method,the solvable sufficient conditions of the finite-time H? filter are given.In the filter design process,the structure of the free matrix is not subject to any restrictions,which makes the conclusions in this chapter less conservative than the existing results.In Chapter 5,the problem of resilient estimation design for nonlinear de-scriptor semi-Markov jump system is discussed.Firstly,the T-S fuzzy model is used to estimate the nonlinear functions,together with the stochastic Lya-punov functional and matrix decoupling techniques,the resilient estimation problem of nonlinear descriptor semi-Markov jump system is considered,the solvable conditions for resilient estimators are given in the terms of linear ma-trix inequality.The estimators can be of full-order or reduced-order.Finally,we give a bio-economic model to illustrate the effectiveness and practicality of the filter design approach in this chapter.The sixth Chapter summarizes the work in this paper,and some further directions are also presented.