Filtering And Control For Some Kinds Of Piecewise Time-delay Nonlinear Systems

In recent years,the problem of controller design for complex systems has been attracting more and more attention since it has important theoretical and practical significance.This dissertation focuses on robust controller design for several classes complex systems under a variety of factors in nonlinear,uncertainties,piecewise linear and time-delay effect with the stability theory of nonlinear systems and some controller design tools.The detailed design processes are given and the effectiveness of the control schemes is illustrated by numerical examples and practical application examples.The main content of this dissertation consists of four parts.(1)Robust Discrete-time Control for Uncertain time-delay Systems with Nonlinearities Under H?lder ContinuityThis section is concerned with the robust discrete-time control for uncertain time-delay systems with nonlinearities and external noises.We consider that all the system matrices include the parameter uncertainties.We supposed that the time-varying delay is unknown with given lower and upper bounds.The stochastic nonlinearities are described by satisfying a class ofaH?lder condition.The problem we addressed is the analysis and design of a stable controller such that,for all the parameter uncertainties,time-delay,stochastic nonlinearities and external noises,the resulting closed-loop system is exponentially stabile.The controller gain can be got by linear matrix inequalities(LMIs).Numerical examples are given to illustrate the effectiveness and verify the proposed theoretical results.(2)Robust Observer-basedH_?Control for Uncertain Discrete Time-delay Systems with Nonlinearities Electric-hydraulic System Under H?lder ConditionIn this section,the robustness andH_?control problems of output dynamic observer-based control for uncertain discrete time-delay systems with nonlinearities under a class of H?lder condition are considered.The parameter uncertainties enter into all the system matrices,the time-varying delay is unknown with given lower and upper bounds,the nonlinearities are described by satisfying a class ofaH?lder condition.The asymptotic stabilization for uncertain time-delay nonlinear system will be guaranteed under no disturbance input.Linear matrix inequality(LMI)optimization approach is used to design the robust observer-basedH_?output dynamic controls.The feedback control and observer gains are got from LMI optimization feasible solution.Electric-hydraulic system is described and used to illustrate the method.(3)Robust discrete-time sliding mode control for uncertain memristor-based piecewise linear systems with time-varying delays and nonlinearitiesThis section investigates the robust discrete-time sliding mode control problem for uncertain piecewise linear system with time-varying delays and nonlinearities,in which uncertain piecewise-constant matrix consist of mismatched uncertain parameters and unknown bounded nonlinear function.By employing the idea of transition function and constructing a new Lyapunov-Krasovskii functional,sufficient conditions are established to ensure the stability of the system dynamics in the specified sliding surface depending on the lower and upper delay bounds.On the basis of the existence condition,the discrete-time sliding mode control law is designed to guarantee the reaching condition.Based on the memristor,the piecewise linear system is given to demonstrate the effectiveness of the proposed discrete-time sliding mode control scheme.(4)Robust observer-based sliding mode H_?control for uncertain piecewise linear systems with time-varying delaysThis section investigates the robust observer-based discrete-time sliding mode H_?control problem for uncertain piecewise linear system with time-varying delays,in which uncertain piecewise-constant matrix consist of mismatched uncertain parameters.By employing the idea of transition function and constructing a new Lyapunov-Krasovskii functional,sliding surface and sufficient conditions are established to ensure the stability of the system dynamics in the specified sliding surface depending on the lower and upper delay bounds.On the basis of the existence condition,the discrete-time observer-based sliding mode control law is designed to guarantee the reaching condition.Numerical examples are given to demonstrate the effectiveness of the proposed discrete-time sliding mode control scheme.Finally,the results of the dissertation are summarized and further research topics are pointed out.