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Improved stability criteria for linear systems with two additive time-varying delays via a novel Lyapunov functional. (English) Zbl 1418.93207

Summary: This paper consider the stability problem of linear systems with two additive time-varying delays. A novel Lyapunov-Krasovskii functional (LKF) is constructed, which consists of the delay-dependent non-integral items and the single-integral items. Based on the newly developed LKF, a stability criterion is derived, which is less conservative than some recent existing ones. Furthermore, to obtain a tighter bound of the integral term, quadratic generalized free-weighting matrix inequality (QGFMI) is used. Finally, a numerical example and an application of the load frequency control for a single area power system are presented to show the effectiveness of the proposed approach.

MSC:

93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93C15 Control/observation systems governed by ordinary differential equations
93C05 Linear systems in control theory
93D30 Lyapunov and storage functions
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