Oscillatority of  Nonlinear  Systems with Static  Feedback

Efimov, Denis; Fradkov, Alexander

doi:10.1137/070706963

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Oscillatority of Nonlinear Systems with Static Feedback

Efimov, Denis; Fradkov, Alexander

2009 • In SIAM Journal on Control and Optimization, 48 (2), p. 618-640

Peer Reviewed verified by ORBi

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https://hdl.handle.net/2268/14360

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10.1137/070706963

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Keywords :

oscillations; robust stability

Abstract :

[en] New Lyapunov-like conditions for oscillatority of dynamical systems in the sense of Yakubovich are proposed. Unlike previous results these conditions are applicable to nonlinear systems and allow for consideration of nonperiodic, e.g., chaotic modes. Upper and lower bounds for oscillations amplitude are obtained. The relation between the oscillatority bounds and excitability indices for the systems with the input are established. Control design procedure providing nonlinear systems with oscillatority property is proposed. Examples illustrating proposed results for Van der Pol system, Lorenz system, and Hindmarsh–Rose neuron model as well as computer simulation results are given.

Disciplines :

Engineering, computing & technology: Multidisciplinary, general & others

Author, co-author :

Efimov, Denis ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation

Fradkov, Alexander; IPME RAS > CSS Lab

Language :

English

Title :

Oscillatority of Nonlinear Systems with Static Feedback

Publication date :

February 2009

Journal title :

SIAM Journal on Control and Optimization

ISSN :

0363-0129

eISSN :

1095-7138

Publisher :

Society for Industrial & Applied Mathematics

Volume :

Issue :

Pages :

618-640

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 12 June 2009

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