Observer-Based Finite-Time Control For Markov Jump Systems

As a typical kind of multi-modal random systems,Markov Jump Systems(MJSs)well overcome the limitation of single mode systems.For the systems affected by environmental mutations,internal component failures and other factors,MJSs can express the randomness of their jump.Because of the strong engineering background,MJSs have been widely used in network control systems,aerospace systems,economic systems and other fields.Many research results of MJSs are proposed based on the infinite time domain at the present stage.However,in the actual engineering systems,the transient performance of the system is also an important part which deserves to be discussed.Based on the observer,this thesis investigates the finite-time control problems of the continuous MJSs under the conditions of the partially unknown transition probability,time delays,actuator failures and uncertain parameters,and makes the whole control system meet the H_? performance index.The main work of this paper is as follows:(1)For the continuous time MJSs with partially unknown transition probabilities and time delays,the finite-time control problems are considered based on the observer under the constraint of the H_? performance index.The free weighted matrix method is used to deal with the unknown part of the transition probability,and the unknown part of the transition probability in the matrix of the Lyapunov function is replaced by the known part to ensure that the acquired linear matrix inequalities(LMIs)are less conservative.The conditions of finite-time stability analysis,the finite-time H_? stability analysis and the controller design for the continuous time MJSs are given.Then,the gain matrices of the state observer and the state feedback controller are obtained by solving the LMIs.Finally,a simulation example is provided to verify the effectiveness of the proposed control algorithm.(2)For the continuous time MJSs with partially unknown transition probabilities and actuator failures,the finite-time fault-tolerant control problems are investigated in this part.By extending the system states,the system is transformed into a generalized description system with jump parameters.Based on the obtained generalized description system,the system observer and controller are designed.By constructing the appropriate Lyapunov function,the sufficient conditions for the system to be bounded in finite time are derived.At the same time,the decoupling technique is employed to deal with the product coupling part of the linear matrix,thus obtaining a set of solvable LMIs.Simulation results show that the proposed sufficient conditions for the finite-time control are effective.(3)For the continuous time MJSs with uncertain parameters and time delays,the finite-time fault-tolerant control problems are studied based on the observer.In case of the actuator failures,the closed-loop error system is obtained by the observer reconstruction.Based on the analysis of the closed-loop error system,the sufficient conditions for the system to be bounded in the finite time are given.By introducing the specific matrices to deal with the time-varying parameter matrices of the system with bounded norms,the robust control algorithm in the case of the finite time is derived,which has certain practical engineering significance.The effectiveness of the method is verified by the simulation example.