Delays-dependent region partitioning approach for stability criterion of linear systems with multiple time-varying delays

Abstract

This paper considers a delay-dependent stability criterion for linear systems with multiple time-varying delays. To exploit all possible information for the relationships among the marginally delayed states (x(t - tau(M)(i)), x(t- tau(M)(i+1))), the exactly delayed states (x(t - tau(i)(t)), x(t - tau(i+1)(t))), and the current state x(t) for each pair (i, i + 1) of time-varying delays, a delays-dependent region partitioning approach in double integral terms is proposed. By applying the Wirtinger-based integral inequality and the reciprocally convex approach to terms resulted from the region partitioning, a stability criterion is derived in terms of linear matrix inequalities. Numerical examples show that the resulting criterion outperforms the existing one in literature. (C) 2017 Elsevier Ltd. All rights reserved.