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Stability and stabilization of nonlinear systems. (English) Zbl 1243.93004

Communications and Control Engineering. London: Springer (ISBN 978-0-85729-512-5/hbk; 978-0-85729-513-2/ebook). xix, 386 p. (2011).
Stability is one of the key properties within systems and control theory. Although many physical systems satisfy some form of stability, a standard requirement for the to-be-designed controller is that it improves the stability. In this research monograph, the authors give an account of the results on stability and stabilizability which have been obtained over the last years. They do this for a large class of systems. Their class of systems include nonlinear ordinary differential equations, but also nonlinear difference equations, and nonlinear delay differential equations. Among others they show that the results on input-to-state stability (ISS) as introduced by E. D. Sontag, see e.g. [Syst. Control Lett. 34, No. 1–2, 93–100 (1998; Zbl 0902.93062)], have been extended a lot. The book gives a clear account of the theory up to today.

MSC:

93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory
93D25 Input-output approaches in control theory
93C10 Nonlinear systems in control theory
93C23 Control/observation systems governed by functional-differential equations
93C57 Sampled-data control/observation systems
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93D15 Stabilization of systems by feedback

Citations:

Zbl 0902.93062
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