Title :
Lyapunov-Krasovskii functional for coupled differential-functional equations
Author :
Gu, Keqin ; Liu, Yi
Author_Institution :
Southern Illinois Univ. Edwardsville, Edwardsville
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 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. Then the stability conditions for systems with time-varying uncertainty are established based on a quadratic Lyapunov-Krasovskii functional. Discretization is used to render the stability conditions to an LMI form.
Keywords :
Lyapunov methods; control system analysis; delay systems; delays; differential equations; functional equations; linear matrix inequalities; stability; time-varying systems; uncertain systems; LMI form; coupled differential-functional equation; lossless propagation model; neutral time-delay system; quadratic Lyapunov-krasovskii functional approach; singular time-delay system; stability problem; time-varying uncertainty; Delay; Differential equations; Linear matrix inequalities; Lyapunov method; Partial differential equations; Propagation losses; Stability; Time varying systems; USA Councils; Uncertainty;
Conference_Titel :
Decision and Control, 2007 46th IEEE Conference on
Conference_Location :
New Orleans, LA
Print_ISBN :
978-1-4244-1497-0
Electronic_ISBN :
0191-2216
DOI :
10.1109/CDC.2007.4434249