Varying Structure Control Of Uncertain Linear Systems With Time-Delay

To the control, it is one of the most challenging subjects for us to try different methods on the object with time-varing, nonlinear, time-delay, varing parameter which presented in the industrial process. Variable structure control with sliding mode(VSCSM) that is brought in 50's is attention-getting because of its ideal robustness. The sliding mode movement of variable structure system holds the invariance for the change of system parameters, outside disturbance, uncertain mode and model uncertainty of the system. It has been broadly used in the field of control with the development of computer technology and produce of high-speed switch circuit. Its flaw is that after the system state getting to the sliding plane, it will produce high frequency chattering around the sliding plane and the control variable of the system will also produce high frequency chattering. In this paper, VSCSM method was used to control a class of time-delay systems with mismatched parametric uncertainties, the existence of linear sliding surface and reaching motion controller were especially studied. The main works are summarized as follows: Firstly, this thesis relatively fully refers to the literature in the field of sliding mode variable structure control , and summarizes the development history and characteristics of sliding mode variable structure control, and particularly introduce the elementary concepts and elementary definitions and design method; discrete-time system variable structure control and the chattering phenomenon of VSC are also studied in this dissertation. Secondly, for a class of time-delay systems with mismatched parametric uncertainties, a sufficient condition for the existence of linear sliding surfaces is given in terms of linear matrix inequalities, based on which the corresponding sliding mode controller is also developed for reaching motion by Lyapunov stability theorem. The obtained results are illustrated by two examples.