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Finite-interval quadratic polynomial inequalities and their application to time-delay systems. (English) Zbl 1437.93017

Summary: This paper proposes two inequality lemmas for the stability analysis of time-delay systems to obtain the stability criteria in terms of linear matrix inequalities from ones in terms of the convex of concave finite-interval quadratic polynomials. The first lemma improves the existing work for the concave finite-interval quadratic polynomial by utilizing the property of a cross point between two tangent lines at the boundaries of the finite interval. The second lemma introduces an inequality for the convex or concave finite-interval quadratic polynomials by decomposing the finite-interval quadratic polynomials into \(a^TMa\), where \(M\) is a \(2\times 2\) block matrix and \(a\) is a vector consisting of a constant and a variable, and by exploiting information on the finite interval. To illustrate the potential of the proposed lemmas, this paper presents feasible regions for the finite-interval quadratic polynomials and maximum time-delay upper bounds for time-delay systems, comparing to those in the literature.

MSC:

93B25 Algebraic methods
93C43 Delay control/observation systems
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
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