Observer-based Finite-time Sliding Mode Control

Markovian Jump Systems(MJSs)is complex stochastic systems composed of a limited number of subsystems,which can effectively describes the mutation of the system mode,and provide a theoretical basis for the description of the system model.The mode switching is controlled by the Markov process.SMC is an effective robust control method,which has a good control effect for dynamical systems subject to parameter uncertainty and external dis-turbance.Due to its advantages such as rapid response and good transient response,SMC is considered to be one of the effective robust control methods for uncertain systems.Finite Time Stability(FTS)is used to analyze the convergence of the system in a short time,and is more suitable for describing the transient behavior of the controlled system.At present,many researches on sliding mode control mostly focus on infinite time stability.The asymptotic stability of infinite time interval cannot meet the practical requirements,because there may appear unsatisfactory transient performance during some time intervals.Due to the influences of cost and technology factors,the system state is not always available in practical applica-tions.Therefore,this paper combines FTS theory with SMC,and discusses H?finite-time control of a class of uncertain systems and Markovian jumping systems with unmeasurable states by sliding mode control.This article is arranged as follows:The first chapter mainly introduces the research background and significance of the sub-ject,state observer,Markovian Jump Systems,Sliding Mode Control,and Finite Time Stabil-ity.The second chapter is the preparation of this article,and gives some related theorems and lemmas.In chapter 3,H?finite-time control for uncertain systems with the unmeasurable s-tate via the sliding mode control(SMC)approach is discussed in this article.Our attention is to design an appropriate finite-time SMC law to attenuate the influences of parametrical uncertainty and external disturbance onto the overall performance of the system under con-sideration.First,an appropriate non-fragile observer-based finite-time SMC law is designed such that the state trajectories can arrive at the specified sliding switching surface(SSS)dur-ing the finite-time interval.Then,finite-time boundness stability(FTBs)is well implemented by partitioning strategy and sufficient conditions are given to realize FTBs for the augment system with H?performance.Finally,a RLC series circuit shows the effectiveness of the proposed SMC approach.In chapter4,mainly discusses H_?finite-time realization for a class of uncertain Marko-vian jump systems(MJSs)with unmeasurable state via sliding mode control(SMC)method.A key question is how to design a suitable SMC approach in a finite-time to reduce the effects of model switching and external interference on the overall performance of the system under consideration.First,by designing a suitable finite-time SMC law based on a non-fragile ob-server,the state trajectory can reach a specified sliding surface(SSS)within given finite-time.Then,by means of time-partitioning strategy,finite-time boundedness(FTBs)in reaching phase and the sliding motion phase are realized respectively,and FTBs criteria are proposed for uncertain MJSs with H_?performance.Second,by solving the corresponding linear ma-trix inequalities(LMIs),controller gains and observer gains are obtained.Finally,an example is used to prove the effectiveness of the proposed method.