Finite-time Control For Markov Jump Systems With Actuator Saturation

The random Markov jump system is a research hotspot in the field of hybrid systems.Markov jump systems are widely used in many dynamic systems with abrupt characteristic,such as communication network systems,economic systems,power systems,etc.A class of special hybrid systems that suffer from random changes in system parameters and structures due to internal discrete events,random failures of components,and environmental abrupt changes can be well described by the Markov jumps.On the other hand,finite-time control has important applications in some practical engineering systems,and its theoretical research has been paid more and more attention.Therefore,it has important practical engineering significance for the research about the finite-time control of Markov jump systems.In recent years,the research on the saturation characteristics of actuators in practical engineering is one of the research hotspots in control theory and application.However,there are few research results on the finite-time control of the Markov jump system with actuator saturation.Therefore,this paper will study the finite time control and controller design of the system for the Markov jump system under the limitation of actuator saturation.The main contents are as follows:1.This paper deales with the problem of finite-time stabilization for discrete-time Markov jump systems with saturated actuators under finite energy perturbation.Firstly,by using the constructed Lyapunov function and the saturated nonlinear processing technique,the problem was analyzed and the sufficient conditions for finite-time boundedness(FTB)and finite-time stabilization(FTS)of the system are proposed.Then the finite-time stabilization controller are designed and implemented by using linear matrix inequalities techniques(LMI).In the end,a numerical example about two modes with discrete-time Markov jump parameters was given to show the validity of the results.2.This paper deals with the problem of finite-time stabilization for a class of discrete-time state-delay Markov jump systems subject to incomplete knowledge of transition probabilities,actuator saturations and unknown but bounded disturbances.A sufficient condition on finite-time boundedness and finite-time stabilization are proposed by using the constructed Lyapunov function and the saturated nonlinear condition.Furthermore,the controller gain based on state feedback is designed by using linear matrix inequality technique.In the end,a numerical example is employed to show the effectiveness of the theoretical results proposed in this paper.3.This paper deals with the problem of stabilization for a class of discrete-time Semi-Markov jump systems subject to actuator saturations.A new sufficient condition on stabilization is proposed by using the saturated nonlinear processing technology,Semi-Markov kernel and the constructed Lyapunov function to a class of discrete-time Semi-Markov jump systems.It should be pointed out that the difficulty of deriving tractable conditions of control designs because of the matrix power.To circumvent the problem,the approach is proposed by introducing external parameters and linear matrix inequality technique.In the end,a numerical example is employed to show the effectiveness of the theoretical results proposed in this paper.