Stabilization of uncertain discrete time-delayed systems via delta operator approach

Abstract

This paper investigates the robust stabilization of uncertain time-delayed systems via delta operator approach. By introducing model transportation, the linear delta operator system with time-varying delays is reformulated into an interconnected system for which the uncertainties can become easy to deal with. Based on a two-term approximation and scaled small gain theorem, a new delay-dependent sufficient condition of state feed-back stabilization for an uncertain delta operator time-delayed system is established by using a novel Lyapunov-Krasovskii functional. The condition obtained can unify some previously suggested relevant methods seen in literature for achieving asymptotic stabilization of both continuous and discrete systems into the delta operator framework. Numerical examples presented explicitly demonstrate the advantages and effectiveness of the proposed method.