A note on relationship between some bounding inequalities in stability analysis of time-delay systems

2017/03/17 by Éva Gyurkovics, Gyurkovics, Eva, Tibor Takács +1
Computer Science · Engineering · Mathematics · #93C23 #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems

paper · pdf · doi:10.48550/arxiv.1703.05936

openalex publication_date 2017/03/17 · openalex created_date 2017/04/07 · openalex updated_date 2026/07/28

Abstract

In this paper, an extension of the generalized free matrix based inequality is introduced in a unified form suitable for the estimation of integrals and sums of quadratic functions. The equivalences of several known variants are shown, including the free matrix based inequalities and its simplified form. Secondly, the relationship between the (simplified) free matrix based estimation and the combination of the Bessel-based inequality with different bounding inequalities affine in the length of the intervals are investigated.

Citations

• Reciprocally convex approach to stability of systems with time-varying delays

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