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Stochastic Stability And Sliding Mode Control Of Markov Jump System With Time-delay

Posted on:2022-05-21Degree:MasterType:Thesis
Country:ChinaCandidate:Z X YuFull Text:PDF
GTID:2518306728975049Subject:Applied Mathematics
Abstract/Summary:PDF Full Text Request
With the rapid development of industrial production,many dynamic systems are complexity and large-scale in the modern control field.Random uncertainties exist in the actual system,such as environmental noise,component failures,random loss,parameter uncertainties and random errors in system input or output.If the statistical properties of a random system are non-after-effects,it can be described as Markov jumping systems(MJSs).The Markov jump phenomenon is ubiquitous in chemical processes,economic systems,manufacturing systems,transportation systems and network control systems.It has become a hot topic of control field in recent years.For MJSs,some research results have been obtained such as stability,stabilization,filtering control and sliding mode control.Among the existing results,only MJSs with one Markov chain are considered,and the transition probability is completely known.However,random phenomena may be described by two or more Markov processes in some economic,flight control and network control systems.The statistical characteristics of random phenomena cannot be fully obtained in the actual system.Therefore,it is more practical significance to study MJSs with two or more Markov processes under incomplete transition probabilities.In this paper,stochastic stability and sliding mode control are studied for discrete-time MJSs with time-delay and two Markov chains under incomplete transition probabilities.The main works as follows:(1)The background of this paper is introduced.Including the research status of Markov jump system,time-delay system,sliding mode control.(2)The stochastic stability is studied for discrete-time MJSs with time-delay and two Markov chains.First,the improved Lyapunov-Krasovskii functional(LKF)is constructed.Based on the properties of transition probabilities and linear matrix inequality(LMI),sufficient conditions are obtained for the random stability of closed-loop systems.Secondly,a modal dependent state feedback controller is designed to obtain a sufficient condition that the system can be stochastic stabilization.Finally,two examples are given to illustrate the effectiveness of the proposed method.(3)The problem of sliding mode control is studied for uncertain discrete-time MJSs with time-delay.First,the discrete integral sliding surface is designed for the system.Base on the delay-fractioning approach,the sufficient conditions are obtained for stochastic stability of the system by considering the parameter uncertainty to meet the matching conditions.Secondly,the sliding mode control law is designed to make the system states reach to the designed sliding mode and keep on it.Finally,a simulation example shows the effectiveness of the proposed method.
Keywords/Search Tags:Markov jump systems, Time-varying delay, Sliding mode control, Stochastic stability
PDF Full Text Request
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