Guaranteed cost control of fractional‐order linear uncertain systems with time‐varying delay

Abstract

Abstract This article is concerned with the guaranteed cost control problem for a class of fractional‐order (FO) uncertain delayed linear systems with norm‐bounded time‐varying parametric uncertainty. Based on whether the states are available or not, guaranteed‐cost state‐based feedback stabilization and guaranteed‐cost observer‐based feedback stabilization for such system are addressed, respectively. By employing the linear matrix inequality (LMI) approach and FO Razumikhin theorem, two delay‐independent guaranteed cost controller design methods and their guaranteed costs are first formulated, respectively, in which sufficient conditions of the state feedback and observer gains are presented in form of LMI. Two numerical examples are presented to demonstrate the effectiveness of the theoretical formulation.