A parametric Lyapunov equation approach to stabilization of discrete-time systems with input delay and saturation

This paper studies the problem of stabilization of discrete-time linear systems with input time-delay and actuator saturation. By exploring some further intricate properties of a recently developed parametric Lyapunov equation based low gain feedback design approach, an alternative approach is proposed to solving the problem by both state feedback and output feedback. This new approach is not only simpler than the methods that are based on the eigenstructure assignment technique, but also provides explicit conditions on value of the low gain parameter to guarantee the stability of the closed-loop system. Furthermore, the delay in the input is allowed to be time-varying in some cases.