Composite Anti-disturbance Control For Singular Markovian Jump Systems With Time-varying Delays

Compared with normal Markov jump systems,the singular Markov jump systems have both the extensiveness of singular systems and the mode uncertainty of Markov jump systems,which can better describe the complex systems in practical engineering applications.Therefore,the singular Markov jump systems are outstanding in modeling.1.Targeting at a series of continuous-time singular Markov jump systems with time-varying delays,the stochastic admissibility of these systems is studied.First,the model of the singular Markov jump systems with time varying delays is given.Then,with the help of Lyapunov stability theory and inequality scaling method,the stochastic admissibility criterion of the singular composite system is given in the form of linear matrix inequality(LMI).Finally,a numerical example is used to verify the obtained conclusions.2.Considering a series of singular time-delay Markov jump systems with multiple disturbances,a composite anti-disturbance control method(disturbance-observer-based control and H_?control)is studied.To commence,by selecting the time-delay-dependent and mode-dependent Lyapunov-Krasovskii(L-K)functional,the H_?performance criterion of the singular composite system is obtained.Then,based on the obtained criteria,the state feedback controller can be designed.Finally,a numerical example is presented to verify the proposed control method.3.For a collection of singular time-delay Markov jump systems with multiple disturbances,a composite anti-disturbance control method(disturbance-observer-based control and L₂-L_?control)is studied.Initially,the L₂-L_?performance analysis criterion of the singular composite system suited for the performance index is given in LMI by selecting a proper L-K functional.Then,according to the obtained criterion,a relatively novel decoupling method is adopted to guarantee that the sufficient conditions for the existence of the state feedback controller can be obtained.After that,a numerical example is shown to testify the correctness and rationality of the designed control scheme.