Dissipative Control For Several Classes Of Singular Markov Jump Systems

Singular systems are more complicated in form than normal systems,and Markov jump systems are widely used in application.Therefore,singular Markov jump systems have attracted much attention from domestic and foreign scholars.In addition,the dissipative theory plays an important role in the study of stability.It can also connect some mathematical tools with physical phenomena.Therefore,the research on the dissipative theory of singular Markov jump systems has theoretical research value and practical application value.In this thesis,based on the dissipative theory,Lyapunov function theory,Markov model and linear matrix inequality method,several kinds of stochastically admissible conditions and related controller design methods are studied.The main research work is as follows:1.For a class of nonlinear singular Markov jump systems with unknown state transition probabilities,a design method of state feedback controller is proposed.Firstly,based on the Lyapunov function theory and the less conservative Willems dissipative theory,and using the classical Lipschitz condition to deal with the nonlinear term,and then considering the quadratic supply rate Q>0,the sufficient conditions for the system to be stochastically admissible and Willems dissipative are given;Then the design method of the state controller is given by the contract transformation method;Finally,Matlab is used to simulate and verify the proposed conclusions.2.For a class of T-S fuzzy singular Markov jump system,a design method of state feedback asynchronous controller is proposed.Firstly,based on the Lyapunov function theory of mode-dependent,and combined with the hidden Markov model,and using the application of the weak infinitesimal operator gives the sufficient conditions for the system to be stochastically admissible and α dissipative;Then the design method of the fuzzy state feedback controller that works asynchronously with the original system is given by the method of linear matrix inequality;Finally,Matlab is used to simulate and verify the proposed conclusions.3.For a class of singular Markov jump systems whose state transition probabilities are completely unknown,a design method of a static output feedback controller is proposed.Firstly,based on the mode-dependent Lyapunov function theory,and considering when each transition probability is completely unknown or the estimated value is known,sufficient conditions are given to make the system stochastically admissible and extended dissipative;Then the design of the static output feedback controller is given by the contract transformation method;Finally,an algorithm is introduced to effectively solve the bilinear matrix inequality,and Matlab is used to simulate and verify the proposed conclusions.