Encyclopedia of Systems and Control

Living Edition
| Editors: John Baillieul, Tariq Samad

Stability: Lyapunov, Linear Systems

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


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.


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