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Keywords:
time-delay systems; state feedback controller; Lyapunov–Krasovskii functional; Wirtinger's inequality; reciprocally convex inequality; linear matrix inequality
time-delay systems; state feedback controller; Lyapunov–Krasovskii functional; Wirtinger's inequality; reciprocally convex inequality; linear matrix inequality
Summary:
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.
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