A memoryless robust stabilizing controller for a class of uncertain linear time-delay systems

Abstract

The memoryless robust stabilization problem is studied for a class of uncertain linear dynamic systems with time-delays in both state and control. The uncertain time-delay systems under consideration are described by state differential equations with time-varying unknown-but-bounded uncertain parameters. A sufficient condition for the existence of a memoryless robust controller is derived and two methods are presented for synthesizing robust control laws for uncertain time-delay systems. One is to transform the robust control problem into a standard H∞ control problem via the equivalent system transformation, and the control law can be obtained by solving an algebraic Riccati equation (ARE). The other method is to transform the sufficient condition into a linear matrix inequality (LMI) problem and the control law can be obtained by solving the LMI. Finally, a numerical example is presented to show the feasibility of the obtained results