Delay-dependent robust control design for uncertain multi-time-delayed linear systems

Purpose – The purpose of this paper is to present a robust control design method for uncertain multi-time-delay linear system. Design/methodology/approach – Delay-dependent stability conditions are given based on time-dependent Lyapunov-Krasovskii functional. By using the key technical lemma (Lemma 1) and the Schur Complement Lemma, the robust control design problem is transferred to the problem of solving several linear matrix inequalities, which can be easily realized by MATLAB Toolbox. Findings – Delay-dependent stability analysis and control design are less conservative than delay-independent one, theoretically. Originality/value – Both state delay and input delay are studied in this paper. Moreover, the uncertainties considered include not only parameter uncertainties, but also noise disturbance.