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

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−τiM), x(t−τi+1M)), the exactly delayed states (x(t−τi(t)),x(t−τi+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.