Sliding Mode And H_? Control For Uncertain Singular Systems With Time-Delay

Singular system is a kind of dynamical systems with wider application backgrounds.They are widely used in electric power system,economic system,electronic network and aerospace system.They have been widely used in practice.Considering system modeling error,exter-nal disturbance,and other factors,uncertainties must exist in the actual system.While the time-delay is a common phenomenon in the objective world and engineering practice,so some problems can only be described with the singular time-delay uncertain system,and its research has significance.Sliding mode control is an effective control method for linear systems,nonlin-ear systems,time-varying systems and uncertain systems.It is an integrated method for control systems.In the sliding mode control,the sliding mode controller is designed to make the system reach the sliding surface.When the certain matching condition is satisfied,the sliding mode on the sliding surface,the perturbation effects are completely robust or invariant,and show more superior characteristics than the general robust control.It is this unique advantage of the sliding mode control that aroused people's wide concern.The sliding mode variable structure control is completely invariant for the uncertainties that satisfy the matching condition.It is one of the advantages of sliding mode control.However,when there are uncertainties and disturbance inputs in the system,it is necessary to control the input disturbance with H_? robust control.How to combine these two control strategies effectively is the main content of this paper.In this paper,we combine two control strategies and study on the corresponding algorithm to solve the problem of a series of uncertain systems with time-delay.The main work of this paper is as follows:1.Design the integral sliding mode surface for normal systems with time-delay and un-certainties.Firstly,it is proved that the sliding mode is completely invariant to the parameter perturbation and external perturbation satisfying the matching uncertainty,and its necessary and sufficient conditions are obtained.Combined with robust H_? control,weak the impact of disturbance.Then the sliding mode stability is analyzed and the relevant sliding mode control law is given.2.Based on the study of uncertain normal systems,the algorithm of uncertain singular systems with time-delay is studied.Firstly,it is proved that the invariable condition of the sliding mode of uncertain singular system is the same as that of the normal system.Secondly,the corresponding integral sliding surface and controller are designed.The controller is divided into two parts.The discontinuous sliding mode controller is used to overcome the existence of uncertain effects,eliminate the matching disturbances;The state feedback H_? controller is used to stabilize and optimize the sliding mode performance and weak the impact of disturbance,making the closed-loop system regular,stable,impulse-free and meeting the H_? control index.