ISS Stabilization of Discrete-time LPV Systems with Interval Time-varying State Delay and Saturating Actuators

Abstract

We address the problem of input-to-state stabilization of linear parameter-varying (LPV) discrete-time systems with delayed state and subject to saturated actuators and to ℓ2-limited disturbance. It is assumed that the time-varying delay belongs to a known interval and its maximum variation between two consecutive instants has limited rate. We propose convex delay-dependent conditions for the synthesis of LPV state feedback controllers that do not require the real-time knowledge of the delay and ensure the local input-to-state stability of the closed-loop system for a set of initial conditions and subject to energy bounded disturbance input signals. The approach is based on rewriting the delayed system as a switched uncertain augmented delay-free system with a dead-zone non-linearity and on the application of the generalized sector condition to deal with the saturating actuators. To illustrate the efficiency of our approach, we present a numerical example.