The Guaranteed Cost Control For Uncertain Switched Singular Systems With Time-delay

With the popularity and appliance of the computer technology and the expansion of the fields of system theory, the theory of the singular system has been developed quickly. Uncertainties inevitably exist in all kinds of physical, industrial and engineering systems, also, the phenomeon of time-delay is frequently appeared. This is usually the source of instability and degradation of performance for the control systems. In 1972, Chang and Peng first proposed guaranteed cost control in the adaptive control. The research of guaranteed cost control has penetrated all areas of control systems, such as linear continuous uncertain systems, discrete uncertain systems, delay systems and singular systems, switched singular systems. Based on Lyapunov stability theory and linear matrix inequality approach, this paper stuties guaranteed cost control problems for uncertain singular system with time-delay. The main contents of this paper as follows:(1) The resilient guaranteed cost control for a class of uncertain descriptor systems with time-delay is studied. The surfficient condition for existence of guaranteed cost state feedback controller is given; then transform the design of guaranteed cost controller problem into linear matrix inequality problem.(2) The guaranteed cost control for a class of switched singular system with input delay is discussed. The surfficient condition for existence of guaranteed cost state feedback controller is given; then transform the design of guaranteed cost controller problem into linear matrix inequality problem.(3) By the Lyapunov stability theory and linear matrix inequality approach, the guaranteed cost control for a class of uncertain switched singular systems with input delay is studied. And sufficient condition for existence of guaranteed cost state feedback controller is given; also transform the design of guaranteed cost controller problem into linear matrix inequality problem.