TY - JOUR

T1 - Oscillatority of nonlinear systems with static feedback

AU - Efimov, Denis V.

AU - Fradkov, Alexander L.

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

KW - Analysis of oscillations

KW - Control of oscillations

UR - http://www.scopus.com/inward/record.url?scp=60649101588&partnerID=8YFLogxK

U2 - 10.1137/070706963

DO - 10.1137/070706963

M3 - Article

AN - SCOPUS:60649101588

VL - 48

SP - 618

EP - 640

JO - SIAM Journal on Control and Optimization

JF - SIAM Journal on Control and Optimization

SN - 0363-0129

IS - 2

ER -