Brief paper: Lyapunov-Krasovskii functional for uniform stability of coupled differential-functional equations

Authors:
Keqin Gu;Yi Liu
Affiliations:
Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL 62026-1805, USA;Department of Mechanical Engineering, ETC Building, 204 East Dean Keeton St., University of Texas, Austin, TX 78705, USA
Venue:
Automatica (Journal of IFAC)
Year:
2009

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Abstract

This article discusses the Lyapunov-Krasovskii functional approach for the stability problem of coupled differential-functional equations. Such systems include, as special cases, many types of time-delay systems, including the lossless propagation model, some neutral time-delay systems and singular time-delay systems. After the general stability theory, the special case of coupled differential-difference equations is discussed, and the necessity for the existence of quadratic Lyapunov-Krasovskii functional is established. Discretization is used to render the stability criterion to an LMI form.