Lyapunov-based stability analysis

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Abstract

This chapter presents generalizations of the direct Lyapunov method to TDSs. In the first section, for general TDSs, the stability notions are defined, and Lyapunov–Krasovskii and Lyapunov–Razumikhin stability theorems are stated. The second section gives a short introduction to linear matrix inequalities. Sections 3.3–3.7 and 3.10 are devoted to delay-independent and delay-dependent stability conditions for linear TDSs. Sufficient conditions are derived in terms of LMIs. Some of the presented ideas may be useful in the nonlinear case. Section 3.9 discusses Lyapunov-based necessary stability conditions for LTI RDEs.

Original languageEnglish
Title of host publicationSystems and Control
Subtitle of host publicationFoundations and Applications
Pages51-133
Number of pages83
Edition9783319093925
DOIs
StatePublished - 2014

Publication series

NameSystems and Control: Foundations and Applications
Number9783319093925
Volume0

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modelling and Simulation
  • Computer Science Applications
  • Control and Optimization
  • Computational Mathematics

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