Stabilization Analysis And Fault Tolerant Control Of Markovian Jump System

In the actual control system,the system parameters may change because of the system itself and the environment.This kind of system is usually modeled by Markovian jump system.Its stability and stabilization based on various controllers have always been the focus of scholars.At the same time,for the sake of security,fault detection,as a kind of fault-tolerant performance,has also attracted much attention.Therefore,it is of great theoretical and practical significance to propose a controller with excellent fault tolerance and make the system less conservative.In this paper,the problems of stababilization analysis and fault tolerant control of different switching systems are studied.Combined with the existing research results of Markovian jump systems and the technology of linear matrix inequality,the following research results are obtained by using two kinds of ways based on controller design and fault detection:(1)For discrete Markovian jump systems(DMJS),the design problem of partially mode-dependent controller of dwell times is studied.Firstly,a kind of partially mode-dependent controller(PMC)experiencing dwell times is proposed,whose stability problem is transformed in to a similar one about another DMJS.Secondly,by exploiting a switched quadratic Lyapunov function(SQLF),sufficient conditions for the designed controller are given in terms of linear matrix inequalities(LMIs).Moreover,more extensions about stabilization realized by fault-tolerant and disordered controllers are considered.Finally,two practical examples are used to show the effectiveness and practicability of the proposed methods.(2)The problem of fault detection problem for a class of discrete-time polytopic uncertain systems is studied.Different from the traditional methods dealing with polytopic uncertainties,not only its values but also the probability distributions are considered.First of all,the above process about polytopic uncertainty is described by applying a Markov process.Then,the original system with polytopic uncertainties becomes to be a Markovian jump system(MJS)without any uncertainty.Accordingly,the fault detection problem is transformed to be a similar one but considered for an MJS.Particularly,the fault detection and isolation(FDI)filter is constructed to be mode-dependent and also said to be polytope-dependent.Since more information of uncertainty is considered,it is claimed that the obtained results are less conservative.Finally,a practical example is used to show the effectiveness and superiority of the proposed methods.