Analysis of Polynomial Systems With Time Delays via the Sum of Squares Decomposition

Analysis of Polynomial Systems With Time Delays via the Sum of Squares Decomposition

We present a methodology for analyzing robust independent-of-delay and delay-dependent stability of equilibria of systems described by nonlinear Delay Differential Equations by algorithmically constructing appropriate Lyapunov-Krasovskii functionals using the sum of squares decomposition of multivar...

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Veröffentlicht in:IEEE transactions on automatic control 2009-05, Vol.54 (5), p.1058-1064
Hauptverfasser: Papachristodoulou, A., Peet, M.M., Lall, S.
Format: Artikel
Sprache:eng
Schlagworte:
Algorithm design and analysis
Decomposition
Delay
Delay effects
Differential equations
Dynamical systems
Functional programming
Linear matrix inequalities
Linear matrix inequality (LMI)
Lyapunov method
Lyapunov-Krasovskii
Methodology
Nonlinear dynamics
Polynomials
Programming
Robust stability
Stability analysis
sum of squares (SOS)
Testing
Time delay
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Beschreibung
Zusammenfassung:We present a methodology for analyzing robust independent-of-delay and delay-dependent stability of equilibria of systems described by nonlinear Delay Differential Equations by algorithmically constructing appropriate Lyapunov-Krasovskii functionals using the sum of squares decomposition of multivariate polynomials and semidefinite programming. We illustrate the methodology using an example from population dynamics.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2009.2017168