Stabilization of linear systems with input delay and saturation-A parametric Lyapunov equation approach

This paper studies the problem of stabilizing a linear system with delayed and saturating feedback. It is known that the eigenstructure assignment-based low-gain feedback law (globally) stabilizes a linear system in the presence of arbitrarily large delay in its input, and semi-globally stabilizes it when the input is also subject to saturation, as long as all its open-loop poles are located in the closed left-half plane. Based on a recently developed parametric Lyapunov equation-based low-gain feedback design method, this paper presents alternative, but simpler and more elegant, feedback laws that solve these problems. The advantages of this new approach include its simplicity, the capability of giving explicit conditions to guarantee the stability of the closed-loop system, and the ease in scheduling the low-gain parameter on line to achieve global stabilization in the presence of actuator saturation.