Stability Analysis And Control For Systems With Markovian Jumping Process

In many practical physical systems,it is unavoidable that system may change or some random disturbance may occur,which would lead to variations in the system struc-ture and parameters.Markovian jump process,as an effective tool of describing the ran-dom factors,has been widely applied to the system modeling to achieve the representa-tion of practical systems with random behaviours.Recently,researches on systems with Markovian jump process have drawn more and more attention in the literature.On the other hand,one of the most fundamental and important topics in control field is the stabil-ity analysis and control of the system.Therefore,this thesis is dedicated to the stability and stabilization for several kinds of systems with Markovian jump process.The main research contents are summarized as follows:This thesis studies the stability analysis and control for a class of discrete-time Markovian jump systems with time delay and external disturbance.By constructing an appropriate Lyapunov functional and establishing a novel summation inequality,less con-servative conditions are obtained to guarantee the stochastic stability of the underlying system.Based on the stability analysis result,an improved bounded real lemma is de-veloped for the H_?disturbance attenuation performance.Further,the state feedback con-troller design is achieved for discrete-time Markovian jump systems with time delay based on the sufficient time-dependent conditions.This thesis studies the stability analysis and control for a class of discrete-time Markovian jump systems with mode asynchronism and partially unknown transition prob-abilities.Due to the stochastic characteristic of Markovian jump process,it is very pos-sible that the asynchronous phenomenon occurs in the system and controller modes.To describe this problem,the conditional probability is introduced to represent the depen-dent relationship between the controller mode and the activated system mode.Since it is difficult to acquire the the full information of more transition probabilities in practice,the partially unknown transition probabilities are taken into account in this research.A necessary and sufficient condition is developed to guarantee the stochastic stability of the resultant closed-loop system and further extended to asynchronous stabilization with partially known transition probabilities.This thesis studies the stability analysis and control for a class of continuous-time semi-Markovian jump systems with generally uncertain transition rates in the sampled-data control framework.By employing a new looped functional and applying a fractional-delayed state concept,sufficient conditions are presented to ensure the stochastic stability of the sampled-data closed-loop system.Based on the stability analysis result,a new theorem is established for the sampled-data controller design of continuous-time semi-Markovian jump systems with generally uncertain transition rates.This thesis studies the stability analysis and control for a class of continuous-time T-S fuzzy Markovian jump systems in the sampled-data control framework.Considering that the premise variables of the fuzzy system and controller are very likely to be mis-matched during the sampling intervals,the mismatched premise variable issue is taken into account in the closed-loop system model.By refining the previous fractional-delayed state concept and constructing a looped functional,which includes more sampling infor-mation,less conservative criteria are developed for the stochastic stability and sampled-data controller design of continuous-time T-S fuzzy Markovian jump systems.This thesis studies the stability analysis and control for a class of continuous-time nonlinear semi-Markovian jump systems in the event-triggered control framework.Due to the fact that the periodic sampling control method causes the redundant data sending problem,we adopt an event-triggered control strategy to save the limited communication resource.According to the event-triggered condition,the closed-loop system is repre-sented by a switched system model.By employing an appropriate Lyapunov functional,a new criterion is obtained for the system's stability and H_?disturbance attenuation perfor-mance,based on which the co-design on the event-triggered controller and the triggering mechanism is achieved.