Stabilization of time-delay nonlinear discrete-time systems with saturating actuators through T-S models

Abstract

In this paper the problem of local stabilization of nonlinear discrete-time systems with time-varying delay and saturating actuators is studied. Firstly, through a fuzzy Lyapunov-Krasovskii (L-K) function, we develop convex conditions to synthesize fuzzy state feedback gain controllers that stabilize the nonlinear system subject to saturating actuators. Next, we introduce a new approach to compute an estimate of the region of attraction where the initial condition sequence is split into two subsequences. The first one is composed of the state vector at the actual instant of sampling, i.e. for k = 0. The second one is composed of the state vectors at the delayed samplings. Then, we propose a convex optimization problem to maximize the estimated region of attraction of the closed loop control system. Finally, we give a numerical example to illustrate the obtained results.