Variable Structure Control Of Singular Bilinear System

Singular bilinear system is a very important class of general nonlinear system,which is the closest with linear system.Many actual field models can be approximated to a singular bilinear system.Because of the invarianve of the sliding mode of the variable structure control system,in recent years,some researchers have studied variable structure control of singular systems,but the study of singular bilinear systems,especially the uncertain time-delay singular bilinear systems of variable structure control has few results.So the sudy of variable stucture control of singular bilinear systems is very significant.In the thesis,the variable structure control of the singular bilinesr systems,the variable structure control of the singular bilinesr systems with time-delay and the variable structure control of the uncertain tmie-delay singular bilinesr systems were studied by using the Lyapunov function,LMI,variable structure control and the switching function.The main content is as follwos.1.The variable structure control and the research background were introduced,and the persent situation and present issues were described.Then it introduced some basic knowledge of singular bilinear systems and variable structure control and summarized some lemmas used in the thesis.2.First,the singlar bilinear systems and uncertain singular bilinear systems of sliding mode variable structure control was studied respectively,then the methods of the front systems were applied to the variable structure control of singular bilinear systems with time-delay.A switching function and a variable structure controller were designed,which can Make the state trajectory of system to reach the switching surface,and ensure the closed-loop system is asymptotically stable.3.The variable structure control of uncertain tmie-delay singular bilinesr systems were studied by using the Lyapunov function and LMI.A switching function and a variable structure controller were designed,which can Make the state trajectory of system to reach the switching surface,and the asymptotical stablility is guaranteed at the same time.