Sunday 21st of January 2018

Improved delay-range-dependent stability criteria for systems with interval time-varying delay and nonlinear perturbations

Hui-Junjun, Zhang-Hexin, Megn-Fei and Zhou-Xin

In this paper, we consider the problem of robust delay-dependent stability for a class of linear systems with interval time-varying delay and nonlinear perturbations. Less conservative robust stability criteria was put forward by using Lyapunov-Krasovskii functional approach and LMI technique. Firstly, the delay interval is partitioned into two subintervals of equal length at the delay-central point and designing new LyapunovCKrasovskii functional for each subinterval. Secondly, the time derivative of a candidate Lyapunov-Krasovskii functional is evaluated in each of these delay segments. Unlike existing methodologies, we using a more tighter integral inequality for dealing the cross-terms that emerge from the time derivative of the Lyapunov-Krasovskii functional and introduce some free weighting matrices for further reduce the conservative. Lastly, based on convex combination technique, a new delay-dependent stability criteria for the system is formulated in terms of linear matrix inequalities (LMIs).Numerical examples are given to show the effectiveness of the proposed approach.

Keywords: Lyapunov-Krasovskii (L-K) functional; Robust stability; Interval time-delay; Integral Inequality; Linear matrix inequality (LMI)

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