Stability Analysis for Time-delay Systems with Nonlinear Disturbances via New Generalized Integral Inequalities
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This paper represents a novel less conservative stability criterion for time-delay systems with nonlinear disturbances. The main purpose is to obtain larger upper bound of the time-varying delay. A suitable Lyapunov- Krasovskii functional (LKF) with triple integral terms is constructed. Then, two new generalized double integral (GDI) inequalities are proposed which encompass Wirtinger-based double inequality as a special case. A simple case of the proposed GDI inequality is utilized to estimate double integral terms in the time derivative of the constructed LKF. Further, an improved delay-dependent stability criterion is derived in the form of linear matrix inequalities (LMIs). Finally, some numerical examples are given to illustrate the improvement of the proposed criteria.
KeywordsGeneralized integral inequalities Lyapunov-Krasovskii functional (LKF) method nonlinear disturbances stability analysis time-delay systems
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