The Control And Robustness Analysis Of Stochastic Jump Systems By Considering Sojourn-time Distributions

In the complex industrial process,dynamic models are proposed to describe the prac-tical system for the better description of the characteristic and features in an accurate way.The stochastic variations of structures result from environment changes,component failures and system delays are common phenomenon in the most practical systems.More-over,stochastic systems has attracted widdely attention and research in the past several decades as an important method to describe the dynamic models,in which stochastic jump systems has received a great improvement and success as its accuracy in modeling practical systems.However,as the improvement of the depth of research and complexity for the stochastic systems,Markov jump systems with sojourn time following exponen-tial distributed or geometric distributed are hardly meet the requirement of the practical systems as its memoryless property,which means the next state of the system is only dependent on the current state instead of all the past ones.This property limits the ap-plication of Markov jump systems.Therefore,Semi-Markov jump systems with sojourn time following any kinds of ditributions are proposed to relax memoryless restriction.which makes Semi-Markov jump systems are capable to modeling more practical systems and becomes a hot topic in recent years.As well known that the system uncertainty,external disturbances and nonlinear sat-uration exist in varies kind of systems as the environment and component characteristic,which may have influonce on the system performance and stability.This paper will con-centrate on the related problems for discrete-time Stochastic:jump systems by designing related controllers in appropriate control schemes and maintaining the corresponding per-formance.Finally,a series of numerical examples and practical examples are applied to verify the effectiveness and feasible of tlle proposed methods.There are several parts for our work in the following:1.For stochastic Markov jump systems with constraints and external disturbances.mod-el predictive control scheme is utilized to design mode-dependent controller to stabilize the system and satisfy the H?/H2 performance index.By using the rolling optimiza-tion property of model predictive control.the first control input is used for the elosed loop system in each sampling time.The transition probability is considered as partly known and sufficient conditions are given by linear matrix inequalities.Finally,a numerical example and financial example are presented to illustrate the effectiveness of the mentioned scheme.2.For stochastic Markov jump systems with actuator saturation and external distur-bances,event-triggered scheme is presented to design the mode-dependent and trig-gered time dependent controllers to stabilize the system and H? performance is used to analysis the robustness of the system.Event-trigger scheme regarded as an aperi-odic driven strategy is consider here instead of a periodic one can reduce the cost of communication in the data transmission.When the triggered condition is satisfied,the event is driven and the controllers renewed,otherwise the controller will use the last state of the system.Finally,a numerical and mass spring damping,system are utilized to analysis the effectiveness and advantage of the proposed scheme.3.For stochastic Semi-Markov jump systems with inevitable parameter uncertainties and external disturbances,robust control scheme is used to design controller to stabi-lize the system and maintain the performance even with disturbances.The analysis process is divided as the mode stays the same and the mode jumps to another.Elapse-time-dependent controllers are designed to reduce the consorvatism of the proposed method and sufficient conditions are given by linear matrix inequalities.Finally,a numerical example and DC motor example are shown to illustrate the proposed approach.4.For stochastic Semi-Markov jump systems with actuator saturation,observer-based controllers are designed to stabilize the system and H? performance index is analyzed.A convex hull set approach is utilized to replace the nonlinear input by a set of linear feedback controllers and the ellipse set is used to obtain the largest feasible region.Finally,a numerical example is utilized to demonstrate the effectiveness of the proposed method.5.As fault process and fault detection process are both modeled as stochastic Semi-Markov jump processes as their characteristics.Active fault tolerant control is applied to design fault detection mode and elapse-time-dependent controllers to achieve ?-error mean square stability.Furthermore,bounded sojourn time is analyzed to reduce the conservatism and bounded sufficient conditions are presentc d by LMIs to analysis the stability and stabilization of the systems.To sum up,this thesis is mainly concerned with the control problem synthesis for stochastic jump systems with considering sojourn time with different distributions.Prac-tical problems such as parameter uncertainty,external disturbances and nonlinear input are considered.T he stabilization and robustness are analyzed under several different kinds of control schemes.Finally,we give a summarize of the whole thesis and the future work is also present for the further development of the control problem for stochastic jump systems.