Dissipative Filtering And Control For Markovian Jump System With Time Delay

Due to the Markovian jump systems with time delay can be used to model various real systems,a great deal of attention has been paid to investigate the delayed Markovian jump systems.As a result,numerous achievement has been reported.However,when there exist external disturbance input in a system,the problem of filtering and control with dissipativity for Markovian jump systems with time delay should be further investigated.In this paper,based on the Lyapunov-Krasovskii functional theory,matrix inequality method and delay-partitioning approach,we study the filtering and control problem for delayed Markovian jump systems.The main contents are summarized as follows:1.Based on event triggered scheme,the dissipative filtering problem for Markovian jump system with time-varying delay is investigated.Firstly,we investigate the filtering prob-lem for delayed Markovian jump systems with nonlinear perturbation and measurement quantization.Employing an integral inequality,a desired filter existence condition is established,under which the filtering error system is stochastically stable and dissipa-tive.A VTOL(vertical take-off and landing)helicopter system is used to illustrate the effectiveness of the proposed scheme.Secondly,we consider a class of discrete-time Markovian jump systems with additive time-varying delays.By constructing a novel Lyapunov-Krasovskii functional and applying matrix inequality method,the desired dissipative filter realization condition is proposed.In addition,the stability condition of delayed Markovian jump systems developed in this paper improved some existing results.2.The problem of dissipative filtering for a class of uncertain Markovian jump systems with mixed delays is investigated,where the uncertainty is assumed to be time-invariant and belongs to a ploytope.By constructing a mode-dependent and parameter-dependent Lyapunov-Krasovskii functional based on delay-partitioning approach,a sufficient con-dition for the existence of a partially mode-dependent dissipative filter is established.An illustrative example of mess-spring is given to demonstrate the effectiveness of the proposed scheme.3.The dissipative filter design problem for a class of discrete-time delayed neural networks with Markovian jumping parameters is studied.Based on the Wirtinger inequality and a refined matrix inequality,a sufficient condition,which guarantees the existence of a reliable filter such that the resulting filtering error system is stochastically stable and extended dissipative,is obtained.The asymptotically stability condition of delayed neu-ral networks developed in this paper is less conservative than some existing results.A biological network is employed to demonstrate the applications of the results proposed.4.We consider the controller design problem for uncertain Markovian jump systems with time-varying delay,where the uncertainty is assumed to be norm bounded.Firstly,we investigate the state-feedback control for neutral systems with semi-Markovian jumping parameters.By applying a more accurate integral inequality and a delay-partitioning approach,sufficient conditions for the existence of a state-feedback controller,which ensures that the resulting closed-loop system is stochastically stable and dissipative,are proposed.Secondly,we concern with the observer-based control problem for de-layed Markovian jump systems with quantized measurements.By constructing a mode-dependent Lyapunov-Krasovskii functional in the base of delay-partitioning approach,sufficient conditions for the solvability of the presented observer-based controller design problem are derived.Illustrative examples are presented to show the improvements and effectiveness of the proposed controllers.