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