Robust Stabilization for DOSs with Time-Varying Delays

Introduction

Goodwin constructed delta operator instead of traditional shift operator for sampling continuous systems in [82]. The proposed method can unify some previous related results of the continuous and discrete systems into the framework of the DOSs framework. A class of systems in delta domain has been studied in [32, 140, 266]. The problem of system instability when the sampling time is fast can be solved by using delta operator model [49]. The delta operator model also has the advantage of better numerical properties at high sampling rates [219]. In contrast to the discrete shift operator approximates, the delta operator approach means that the Euler derivative can lead to a quasi-continuous time s-domain model for high sampling frequencies, see for example, [54] and the reference therein. The robustness problem for some DOSs with parametric uncertainties also has been investigated. There are a few papers consider the stability of DOSs such as [214] and [215], and H _∞ control problem has been reported in [52], which proved that the discrete-time controller approach to the continuous-time systems using delta operator.