Stability of Actively Controlled Structures with Actuator Saturation

Abstract

Because of the stochastic nature of earthquakes and limited capacities of actuators, it is conceivable that the actuators used for the control of civil engineering structures may be saturated during strong earthquakes. In this paper, the stability of actively controlled linear structures under a variety of popular control methods during actuator saturation is investigated. Sufficient conditions to guarantee the asymptotic stability of the structure during actuator saturation are examined and discussed. These conditions involve the solution of a system of simultaneous linear matrix inequalities (LMI). A simple and efficient computer code to solve a system of LMI, based on the MATLAB LMI toolbox, is presented for use by the readers. Based on sufficient conditions, a method for designing general controllers, that guarantee asymptotic stability during actuator saturation, is presented. It is shown analytically that Lyapunov controllers,