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 − τ i M ) , x ( t − τ i + 1 M ) ), the exactly delayed states ( x ( t − τ i ( t ) ) , x ( t − τ 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.

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