Research On Finite-time Control Of Singularly Perturbed Switching System

With the rapid development of industrial system,the multi-time scale characteristics coupled by fast-varying dynamic and slow-varying dynamic occur frequently,this difference in the rate of change is lead to ill-conditioned numerical problems in the modeling,analysis and design of the system.Singularly perturbed system comes into being and provides an effective tool to deal with this kind of problem.On the other hand,as a kind of dynamic hybrid system,the switched system consisting of a limited number of subsystems and a switching rule that controls the operation of the subsystems is widely used in various fields because of its powerful modeling capabilities.Event-triggered control sets triggering-rules based on system states requirements to improve communication efficiency.Fuzzy control is used as a tool to approximate nonlinear functions with arbitrary precision.In practical applications,more attention is paid to the transient behavior of the system in finite-time intervals,i.e.,finite-time stability.The finite-time control of singularly perturbed switched system is discussed by combining the theories of finite-time fuzzy control and event-triggered strategies.The main research contents are as follows:Firstly,the finite-time control of fuzzy switched singularly perturbed system is studied.First of all,different from Lyapunov stability,finite-time stability is set up to analyze the transient performance,where the system state remains within the fixed thresholds for a given finite-time interval.Secondly,in the face of singular perturbation,a Lyapunov function with fuzzy switched singular perturbation parameter dependent is firstly introduced in the sense of finite-time.Then,inspired by the mode-dependent average dwell time switching rule,a developed finite-time stability criterion is derived to the corresponding system to eliminate an ill-conditioned issue caused by the small singularly perturbed parameter.Moreover,a new fuzzy control strategy is proposed to ensure the predefined finite-time stability.Finally,the feasibility of the main results is proved by an inverted pendulum model.Secondly,the finite-time control of Markov switching singularly perturbed system is studied.Where the stochastic process is regulated by a Markov chain with partially unknown transition probabilities.First,fast-varying dynamic and slow-varying dynamic are considered in the modeling,and the corresponding Markov switching model with a singularly perturbed parameter is built in a unified framework.Then,the ill-conditioned problem caused by a small singular perturbation parameter is prevented by developing a finite-time stability criterion for the resultant system.Furthermore,feasible conditions are derived for the desired finite-time state feedback controller by using matrix inequalities that are independent of the singularly perturbed parameter.Finally,a numerical example is applied to illustrate the effectiveness of the described control strategy.Thirdly,the finite-time event-triggered control of fuzzy Markov switched singularly perturbed system is studied.First of all,T-S fuzzy strategy is adopted to characterize the related nonlinear Markov switched singularly perturbed model.The control object is to make sure that the system states remain within a bounded domain during a fixed time-interval.Moreover,a mode-dependent event-triggered scheme is constructed to reduce the communication burden and save the network bandwidth.Based on the new Lyapunov function,a finite-time stability criterion is derived for the corresponding system to avoid an ill-conditioned issue owing to a small singular perturbation parameter.Then,the mode-dependent fuzzy controller gain and the event-triggered parameter are designed under the framework of partially unknown transition probabilities.Finally,the finite-time event-triggered control strategy is verified by an improved DC motor model.