Robust stability analysis and controller design with quadratic Lyapunov functions. (English) Zbl 0803.93032

Corless, Martin

Zinober, Alan S. I. (ed.), Variable structure and Lyapunov control. Berlin: Springer-Verlag. Lect. Notes Control Inf. Sci. 193, 181-203 (1994).

Lyapunov’s direct method is a well established approach to analyse the stability of an equilibrium state in classical nonlinear systems theory. Only recently, however, Lyapunov theory has newly attracted considerable interest in the context of a new type of problems, namely robust stability of uncertain linear or nonlinear systems. Robust stability means asymptotic stability in the presence of a large set of allowable uncertainties.
The paper overviews some main results of international research activities in this field, including a large list of references mainly over the past decade. The paper is confined to methods using a common quadratic Lyapunov function, with a focus on linear uncertain systems. The design of robust feedback control is still a broad field for future research. The few methods presented all require full state feedback.
For the entire collection see [Zbl 0782.00041].

Reviewer: D.Franke (Hamburg)

MSC:

93D09	Robust stability
93B12	Variable structure systems
93B51	Design techniques (robust design, computer-aided design, etc.)
93D05	Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93D30	Lyapunov and storage functions

Keywords:

quadratic Lyapunov function; linear uncertain systems