Control of constrained discrete-time systems with time-varying state delay

In this chapter, we present the stabilization problem for the class of discrete-time state-delayed systems under saturating actuators and state-constraints. We exploit an augmented model representation that allows handling the variation rate of the delay. We show that such an approach is suitable to cast specific stabilization problems, including LPV, quasi-LPV, switching, and robust control. We use the local stability to search for a region of initial conditions, as large as possible, ensuring closed-loop trajectories converge to the origin without leaving the respective region of attraction. The proposed conditions are based on the Lyapunov theory and are formulated in terms of convex optimization procedures. A key issue to obtain the conditions is the generalized sector condition. Some examples illustrate the methodology and serve to compare the proposed design methods, making clear the differences between the specific stabilization cases.