Control Of Several Types Of Linear Systems

This paper discusses the stability of linear system in three different situations,which are finite-time stability.the stability of linear systems with saturation actuators and the stability of linear systems with repetitive controller.We give the necessary and sufficient conditions or sufficient conditions of their stabilities by using linear matrix inequalities (LMIs) methods. And calculate the necessary and sufficient condition or sufficient condition for feedback stabilizations of these systems. Main content as follows:First:Based on the linear matrix inequalities (LMIs) method, we give the necessary and sufficient conditions for finite-time stability of discrete linear system,and the sufficient conditions for finite-time boundedness.And then we get the necessary and sufficient con-ditions or the sufficient conditions of finite-time stability, finite-time boundedness for the closed-loop systems is obtained by state feedback and output feedback.Second:The state feedback stabilization for discrete singular systems with input sat-uration actuators is discussed.Then feedback stabilization for the discrete singular time-delay systems with disturbance is given.Finally,we obtain the solution of the state feedback stabilization for the discrete singular time-delay systems with disturbance and input sat-uration actuators.Third:Repetitive controller design for linear discrete system with time-varying input delay.We find a state feedback controller to make the system become closed-loop.Then,combine the repetitive controller with the closed-loop system by adding state variables.The stability of the whole system is represented by a linear matrix inequalities.The repetitive controller design for linear discrete system is transformed to an optimization problem via reformu-lating the linear matrix inequalities.