Finite-time Constrained Control And Filtering For Markov Switching Systems

As an important branch of the hybrid systems,the Markov switching systems have attracted many domestic and overseas scholars because of their simple and convenient mathematical expression and extensive applications in the fields of power systems,circuit network systems,aerospace systems,robot mechanical systems,economic systems and manufacturing industry and so on.Based on the existing research results,this dissertation studies the finite-time constrained control and filtering problem for Markov switching systems,in which the constraints may be caused by mode detecting and imperfect network transmission.The main contents are focus on the finite-time l₂-l_?tracking controller design,finite-time asynchronous H_? filter design,finite-time asynchronous l₂-l_?filter design and the details are given as follows:1.The problem of finite time l₂-l_?tracking control for a class of repeated scalar nonlinear systems with Markov switching is researched.The mode information of the considered systems is partly usable and follows a certain Bernoulli distribution of white noise sequences.The main purpose is to design a state feedback controller such that the systems under consideration can track a given signal within a finite time and satisfy a certain l₂-l_?performance.First,some sufficient conditions for the existence of a feasible state feedback controller are obtained by using the mode-dependent diagonally dominant Lyapunov functional method.Based on these conditions,a state-feedback controller can be constructed by using an improved matrix decoupling method.Finally,the validity of the proposed method is verified by a numerical example and an economic model.2.The finite-time asynchronous H_? filtering problem for a class of discrete time networked Markov jump systems is studied,in which the unreliable communication links between the system and filter are fully taken into account,which may lead to the simultaneous occurrences of packet dropouts and time delays.Additionally,sensor nonlinearity and nonsynchronous modes are also considered.Two random variables are used to describe the random occurrence phenomenon among them,which makes our system model more versatile than other literature.Based on the finite-time stochastic theory,the criterion for the existence of the asynchronous filter is obtained,which can ensure the filtering error system is of mean-square stochastically finite-time bounded and satisfies the desired H_? performance index.By using this criterion and applying the improved matrix decoupling method proposed in the third chapter for controller design to the filter design problem,the proposed asynchronous filter design method has lower conservativeness.Finally,the numerical examples and the PWM-driven boost converter model are given to illustrate the superiority and feasibility of the proposed method.3.Based on the results obtained in 2,we extend such results to the networked nonlinear Markov switching system,and discuss its finite time asynchronous l₂-l_?filtering problem,in which the transmission constraint problem of the network,sensor nonlinearity and the asynchronous phenomenon between the system mode and the filter mode are also considered.Based on the finite-time stability theory and combining the Takagi-Sugeno fuzzy model,the characteristics of the nonlinear system are deeply dissected,the finitetime bounded and l₂-l_?performance of the filtering error system are well analyzed,and the asynchronous filter design method is given.Finally,a numerical example and an inverted pendulum model show that the proposed design method is available.