State-feedback stabilization of linear systems subject to time-varying input delays, actuator saturation, and bounded disturbances

The stabilization problem of linear systems subject to time-varying input delays, actuator saturation, and norm-bounded disturbances is studied in this paper using the linear state-feedback control law. Delay-dependent matrix inequality conditions are derived to guarantee the uniform boundedness of solutions of the closed-loop systems. By exploiting the inequality constraints of initial conditions, an analytic expression for the admissible maximum bound of disturbances is obtained using the geometric principle, which ensures the existence of a non-empty set of initial conditions. Moreover, an optimization problem is formulated further for the maximization purpose of the admissible maximum bound of disturbances and the size of the set of initial conditions. The effectiveness of proposed design techniques is demonstrated by a numeric example.