New inclusion sets for singular values.

In this paper, for a given matrix [Formula: see text], in terms of [Formula: see text] and [Formula: see text], where [Formula: see text], [Formula: see text], some new inclusion sets for singular values of the matrix are established. It is proved that the new inclusion sets are tighter than the Gersgorin-type sets (Qi in Linear Algebra Appl. 56:105-119, 1984) and the Brauer-type sets (Li in Comput. Math. Appl. 37:9-15, 1999). A numerical experiment shows the efficiency of our new results.

Improved delay-dependent stability analysis for neural networks with time-varying delays.

In this paper, the problem of delay-dependent asymptotic stability analysis for neural networks with time-varying delays is considered. A new class of Lyapunov functional is proposed by considering the information of neuron activation functions adequately. By using the delay-partitioning method and the reciprocally convex technique, some less conservative stability criteria are obtained in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are given to illustrate the effectiveness of the derived method.