Delay-partitioning approach for systems with interval time-varying delay and nonlinear perturbations

This paper considers the problem of robust stability for a class of linear systems with interval time-varying delay and nonlinear perturbations. Less conservative stability criteria was put forward by using delay-partitioning approach. By decomposing the delay interval into multiple equidistant subintervals, new Lyapunov-Krasovskii (L-K) functional contains some triple-integral terms and augment terms which are introduced on these intervals, thus resulting in being much less conservative than most existing results in the literature. In addition, in deriving the stability conditions in linear matrix inequality (LMI) framework, neither model transformations nor superfluous free-weighting matrix are employed for dealing the cross-terms that emerge from the time derivative of the L-K functional; instead, they are dealt using tighter integral inequalities which only contain a minimal number of slack matrix variables. Numerical examples are given to demonstrate the effectiveness of the proposed approach.