Encyclopedia of Systems and Control

Living Edition
| Editors: John Baillieul, Tariq Samad

Feedback Stabilization of Nonlinear Systems

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DOI: https://doi.org/10.1007/978-1-4471-5102-9_85-1
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Abstract

We consider the simplest design problem for nonlinear systems: the problem of rendering asymptotically stable a given equilibrium by means of state feedback. For such a problem, we provide a necessary condition, known as Brockett condition, and a sufficient condition, which relies upon the definition of a class of functions, known as control Lyapunov functions. The theory is illustrated by means of a few examples. In addition, we discuss a nonlinear enhancement of the so-called separation principle for stabilization by means of partial state information.

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© Springer-Verlag London 2013

Authors and Affiliations

  1. 1.Department of Electrical and Electronic EngineeringImperial College LondonLondonUK