Robust Delay-Dependent H∞ Control for Uncertain Structural Systems With Actuator Delay

Abstract

This paper is concerned with the design of a robust, state-feedback, delay-dependent H∞ controller for an active vibration control of seismic-excited structural systems having actuator delay, norm bounded uncertainties, and L2 disturbances. The norm bounded uncertainties are assumed to exist in variations of structural stiffness and damping coefficients. Based on the selection of Lyapunov–Krasovskii functional, first a bounded real lemma (BRL) is obtained in terms of linear matrix inequalities (LMIs) such that the nominal, time-delay system is guaranteed to be globally asymptotically stable with minimum allowable disturbance attenuation level. Extending BRL, sufficient delay-dependent criteria are developed for a stabilizing H∞ controller synthesis involving a matrix inequality for which a nonlinear optimization algorithm with LMIs is proposed to get feasible solution to the problem. Moreover, for the case of existence of norm-bounded uncertainties, both the BRL and H∞ stabilization criteria are easily extended by employing a well-known bounding technique. Then, a cone complementary algorithm is also utilized to solve the nonconvex optimization problem. By use of the proposed method, a suboptimal controller with maximum allowable delay bound, uncertainty bound and minimum allowable disturbance attenuation level can be easily obtained by solving the proposed convex optimization technique. A four-degree-of-freedom uncertain structural system subject to seismic excitations is used to illustrate the effectiveness of the approach through simulations. Simulation results, obtained by using real time-history data of Kobe and Kocaeli earthquakes show that the proposed controller is very effective in reducing vibration amplitudes of storeys and guarantees stability at maximum actuator delay and parametric uncertainty bound.