Delay-dependent H∞ controller design for seismic-excited structures with actuator delay under consideration of actuator saturation

This paper studies the design of a state-feedback delay-dependent H∞ controller for vibration attenuation problem of a seismic-excited structural system having time-varying actuator delay, L2 disturbances and actuator saturation. First, sufficient delay-dependent stability criteria are derived by choosing a Lyapunov-Krasovskii functional candidate based on matrix inequalities for a stabilizing H∞ synthesis. To overcome the bilinear matrix inequality problems involved in the delay dependent conditions; a cone complementary linearization method is used to find a feasible solution set. The proposed method utilizes convex description of nonlinear saturation phenomenon by means of convex hull of some linear feedback which leads to a few additional ellipsoidal conditions in terms of linear matrix inequalities (LMIs). By use of the proposed method, a suboptimal controller with maximum allowable delay bound and minimum allowable disturbance attenuation level can be easily obtained by a convex optimization technique. The effectiveness of the proposed controller is illustrated through simulations of the responses of a-four-degree-of-freedom structural system under seismic excitations. Simulation results show that, in spite of the actuator saturation, the designed controller is all effective in reducing vibration amplitudes of storeys and guarantees stability at maximum actuator delay.