Non-differentiable Delay-interval-dependent Exponentially Passive Conditions for Certain Neutral Integro-differential Equations with Time-varying Delays

Watcharin Chartbupapan, Thongchai Botmart, Kanit Mukdasai, Narongrit Kaewbanjak

Abstract

The problem of non-differentiable delay-interval-dependent exponentially passive conditions for certain neutral integro-differential equation with time-varying delays is studied. The time-varying delays, being continuous functions, are under the allowed interval delays, therefore the lower and upper bounds of time-varying delays are accessible. But the condition on the derivatives of the distributed and discrete interval time-varying delays are eliminated. These conditions are interested on distributed and discrete delays for the equation. By applying decomposition technique of coefficient constant, descriptor model transformation, new class of augmented Lyapunov-Krasovskii functional, Leibniz-Newton formula, improved integral inequalities, utilization of zero equation and Peng-Park's integral inequality, new delay-interval-dependent exponentially passive conditions are in form of linear matrix inequalities (LMIs). Furthermore, improved delay-dependent stability conditions for certain neutral differential equation with time-varying delays are presented. Numerical examples represent the improvement and effectiveness of results over another research.