Delay-dependent local stabilization of uncertain input-delayed systems with actuator saturation and bounded disturbances

A matrix inequality approach is proposed for local stabilization of a class of uncertain linear systems subject to time-varying input delays, actuator saturation, and norm-bounded disturbances. Delay-dependent stability and stabilization conditions by using the linear state-feedback control law are obtained to guarantee the uniform boundedness of solutions of the closed-loop systems. Besides, an admissible maximum bound of disturbances can be ascertained to ensure the existence of a non-empty set of initial conditions. An optimization framework is formulated further for the maximization purpose of the admissible upper bound of disturbances and the size of the set of initial conditions. A numerical example is provided to demonstrate the effectiveness of proposed design techniques.