Uncertain Time-delay System Robust H_ ¡Þ State Feedback Control

The problem of robust H_∞control is an active field in the study of control. Its abundant theory and advanced approaches provided effective facilities to resolve the controlling problems which emerges continuously in the scientific and technological field nowadays.At the same time,we acquire a succession of achievements and many successful applications were obtained in some engineering science.The introduction of the linear matrix inequality(LMI) offers an effective instrument to resolve the analysis of many controlling problems. The theory of robust H_∞control considers the combination of the uncertainty of parameters and the external disturbance,compensated the defect of requiring precious mathematical model.Because of the theory of robust H_∞control, the analysis and integration of the systems get more effective and practical. Since the time delay is frequently a source of instability and encountered in various engineering systems such as chemical processes,long transmission lines in pneumatic systems,etc.,the study of time delay systems has received considerable attention over the past years.In this paper,we present the mathematical model for the uncertain time-varying linear systems.We discuss the robust H_∞control for continuous uncertain time-varying and the discrete time uncertain systems.According to the content,we separate this paper into three contents:Section 1:We recommend the significance and actuality of the robust H_∞control in the introduction.Section 2:In this section,we discuss the problem of robust and non-fragile H_∞control for uncertain time-varying linear systems with delay.Based on the method of linear matrix inequality(LMI),we get the existence of the sufficient condition of non-fragile controller.At the same time,using the Schur complements and some transformation of matrix,we transform the obtained sufficient condition to an LMI form.Section 3:We discuss the robust H_∞control for a class of discrete time uncertain systems in this section.Based on the quadratic stability theory and the properties of matrix inequality,the sufficient condition for a robust H_∞controller was derived.