| Uncertainties and time-delay are common in engineering practice.It is of great theoretical and practical significance to consider them during the design and implementation of control systems.Tracking control of linear time-delay systems is studied.Further,based on the interval observer,the stabilization of linear time-delay uncertain positive systems and one-sided Lipschitz nonlinear uncertain system with time-delay are investigated in this paper.The main research contents are as follows:First,the disturbance attenuation and tracking control for linear systems with time-delay are dealt with.A differential operator is constructed by Hamilton-Caylay Theorem such that the tracking problem is converted to a stabilization problem.A control law is designed such that the output of the closed-loop system is able to track the reference signal and effectively reject the disturbance.Finally,an example is given to illustrate the validity of the design approach.Secondly,for continuous and discrete linear uncertain positive systems with time delays,by using the theory of positive system and the theorem of disk region,the interval observers are designed,respectively,and control laws are acquired based on the states of interval observers.Then,it is proved that the control laws can make the closed-loop systems positive and asymptotically stable,respectively.Two simulation examples are given to demonstrate the effectiveness of the proposed method.Finally,sufficient conditions for stabilization a class of one-sided Lipschitz uncertain nonlinear systems with time-delay are given by using linear matrix inequalities.Next,the interval observer for system is designed,and a control law is acquired based on the state of interval observer.Then by applying differential inclusion system theory,we prove that the closed-loop system is asymptotically stable with the help of the convex hull Lyapunov-Krasovskii functional.The effectiveness of the design method is verified by a simulation example. |
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