Encyclopedia of Systems and Control

Living Edition
| Editors: John Baillieul, Tariq Samad

Stability: Lyapunov, Linear Systems

Living reference work entry
DOI: https://doi.org/10.1007/978-1-4471-5102-9_194-1

Abstract

The notion of stability allows to study the qualitative behavior of dynamical systems. In particular it allows to study the behavior of trajectories close to an equilibrium point or to a motion. The notion of stability that we discuss has been introduced in 1882 by the Russian mathematician A.M. Lyapunov, in his Doctoral Thesis; hence, it is often referred to as Lyapunov stability. In this entry we discuss and characterize Lyapunov stability for linear systems.

Keywords

Linear systems Equilibrium points Motions Stability Eigenvalues 
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Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

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