Simultaneous Stabilization For Nonlinear Time-Delay Systems With Uncertain Parameters

In control theory,Time delay exists not only in the state of the system,but also in the external input,or in the disturbance or in the output,and the time delay system refers to the state change of the system.In the actual industrial production,the control system often has time delay,and there is uncertainty in the process of control,so it is of great theoretical and practical significance to consider uncertainty and delay in the control design.In addition,stabilization problem also is a significant problem in control field.The disturbances present in various system including circuit system,industry system,and life system,hence whether can we achieve the state we expect under the existing of disturbances is a stabilization problem.In practice,however,a system generally consists of several sub-systems,and leading all sub-systems stabilization is a meaningful problem.In this paper,we mainly study the control problem of nonlinear uncertain systems.In addition,based on the LyapunovKrasovskii stability theory we develop a family of simultaneous stabilization controllers for single-input(multi-input)nonlinear systems with uncertainties.The main contents of this paper are as follows:First,aim at a nonlinear system with uncertain parameters,the necessary and sufficient conditions of existing control Lyapunov functions for this kind of systems are presented.Furthermore,based on Lyapunov stability theory,a feedback controller is designed to make the system asymptotically stable.Simulation result is shown that the proposed method is effective.Secondly,aim at a set of signal-input nonlinear systems with time delay and uncer-tainty,based on Lyapunov-Krasovskii functional,two kinds of control laws are designed.We prove that the proposed control laws can make the closed-loop systems simultaneous stabilization.Two simulation examples are shown that the proposed methods are correct and effective,respectively.Finally,aim at a set of multi-input nonlinear systems with time delay and uncertainty,using Lyapunov-Krasovskii functional and linear matrix inequality theory,the sufficient conditions of simultaneous stabilization for this kind of systems are acquired.Further,a control law is designed such that a set of the closed-loop systems are simultaneous stabilization.Simulation examples are given to show that the proposed methods correctness and effectiveness.