Non-Fragile Finite-Time Controller Design For Lipschitz Nonlinear Systems

In the actual control system analysis and design process,the nonlinear control problem has received widespread attention.As a special nonlinear system,people's research on Lipschitz nonlinear systems has become more and more intensive,such as stability analysis,controller and filter design,state estimation and fault diagnosisOn the other hand,the stability of the system is crucial to the research in the field of control.In general,we consider the stability of the first-time Lyapunov asymptotic stability;but in many practical projects,we often need to consider the transient characteristics of the system,such as considering stability,stability and related control problems in short time interval.Compared with Lyapunov asymptotic stability,the finite-time stability considers the transient performance and short-time control of the system more,which is more theoretical and practical for a short-running system Combined with the Lipschitz nonlinear system,this paper explores and studies the finite-time non-fragile control problem.The specific research contents are as follows(1)For a class of uncertain Lipschitz nonlinear systems with t:ime-delay,a solution for the related content of non-fragile H?.control is designed.By selecting the appropriate Lyapunov function and combining the linear matrix inequality(LMI)method,a suitable non-fragile controller is designed to make the closed-loop control system be stable in finite time interval and satisfy the sufficient condition of the given performance index.Then,the gain of the non-fragile controller is solved and transformed into an optimal solution problem.(2)For the nonlinear systems with Lipschitz conditions,the solution method for non-fragile L2-L? control problems is discussed,and sufficient conditions for the existence of gain solutions for non-fragile time-delay state controllers are given Furthermore,the problem of the controller gain solution is transformed into an optimization solution problem.(3)For a class of time-delay Lipschitz nonlinear systems,the uncertainties,delays and unmeasurable states of the system are considered.By designing the non-fragile H? observer-based controller,Sufficient conditions for the Lipschitz nonlinear closed-loop system to finite-time stability and meet the given performance index are designed and given(4)When the system state is unmeasurable,the observer-based non-fragile guaranteed cost controller problem is analyzed and solved.By designing suitable non-fragile guaranteed cost controller and state observer,Sufficient conditions for the closed-loop system to be stable for a limited time and to satisfy a given performance index are designed and given.The gains of non-fragile controller and non-fragile observer are solved by a linear matrix inequality toolbox and an optimal solution methodThe main results of the main contents of each chapter of this paper verify the feasibility and effectiveness of the design method through digital simulation.