Kybernetika 59 no. 4, 633-654, 2023

An improved delay-dependent stabilization criterion of linear time-varying delay systems: An iterative method

Venkatesh Modala, Sourav Patra and Goshaidas RayDOI: 10.14736/kyb-2023-4-0633

Abstract:

This paper presents delay-dependent stabilization criteria for linear time-varying delay systems. A less conservative stabilization criterion is derived by invoking a new Lyapunov-Krasovskii functional and then, extended reciprocally convex inequality in combination with Wirtinger's inequality is exploited to obtain an improved stabilization criterion where a set of nonlinear matrix inequalities is solved by applying the cone complementarity algorithm. The proposed stabilization technique transforms a non-convex problem into a nonlinear trace minimization problem which is solved by an iterative approach. Numerical examples are considered to demonstrate the effectiveness of the proposed stabilization criteria and the presented iterative algorithm outperforms some existing results.

Keywords:

linear matrix inequality, time-delay systems, Lyapunov-Krasovskii functional, state feedback controller, Wirtinger's inequality, reciprocally convex inequality

Classification:

93Dxx, 93B52

paper.pdf

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