ISS Robust Stabilization of State-Delayed Discrete-Time Systems With Bounded Delay Variation and Saturating Actuators

We address the problem of robust input-to-state stabilization of parameter-varying discrete-time systems with time-varying state delay, saturating actuators, and subject to ℓ
₂
-limited disturbance. It is assumed that the delay belongs to a known interval and its maximum variation between two consecutive instants is taken into account. The proposed convex delay-dependent conditions for the synthesis of robust state feedback controllers ensure local input-to-state stability of the closed-loop system for a set of initial conditions and for energy-bounded disturbance signals. However, the computed controllers do not require the real-time knowledge of the delay. The approach is based on the rewriting of the saturating and delayed system in terms of a switching uncertain augmented delay-free system with a dead-zone nonlinearity and on the application of the generalized sector condition. To illustrate the efficiency of our approach, we compare it by means of numerical examples with others found in the literature.