ROBUST H-INFINITY CONTROLLER-DESIGN FOR TIME-VARYING UNCERTAIN LINEAR-SYSTEMS WITH TIME-VARYING STATE AND CONTROL DELAYS

The robust H-infinity control problem for time-varying uncertain linea r systems with time-varying state and control delays is considered. Ba sed on the Riccati equation approach, we design a robust H-infinity li near time-invariant state feedback control law, which stabilizes the s ystem and reduces the effect of the disturbance input on the controlle d output to a prescribed level for all admissible uncertainties. A suf ficient condition for the existence of the robust H-infinity controlle r is derived and two synthesis methods are presented for a robust H-in finity control law to uncertain time-delay systems. One is to construc t a robust H-infinity control law by an equivalent linear time-invaria nt structural description for the sufficient condition and the control law can be obtained by solving an algebraic Riccati equation (ARE). T he other method is to transform the sufficient condition into a linear matrix inequality (LMI) problem and the control law can be obtained b y solving the LMI. A numerical example is presented to illustrate the obtained results.