Robust memoryless H∞ control for uncertain linear time-delay systems

The problem of quadratic stabilization and robust H^∞ controller design for a class of linear time-varying uncertain dynamic systems with delayed state and control are studied via a Riccati equation approach. A static state feedback controller which stabilizes the plant and reduces the effect of the disturbance input on the controlled output to a prescribed level for all admissible time-varying uncertainties is presented and a sufficient condition for the existence of a robust H^∞ controller is derived. Then the sufficient condition is transformed into a linear matrix inequality (LMI) problem and the control law can be obtained by solving LMIs