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Necessary and sufficient conditions for quenching auto-oscillations in nonlinear systems. (English. Russian original) Zbl 0890.93044
Dokl. Math. 53, No. 2, 309-311 (1996); translation from Dokl. Akad. Nauk 347, No. 3, 324-326 (1996).
The authors consider a one-dimensional control system governed by the equations $A(D)x(t) = B(D)v(t), \qquad v(t) = F(u),$ where $$x$$ is the output variable and $$v$$ is the controlling force nonlinearly depending on the control function $$u$$ and $$A(D)$$, $$B(D)$$ are differential operators. Under various nonlinear characteristics of $$F(u)$$ necessary and sufficient conditions to quench auto-oscillations in the above system are given.
##### MSC:
 93C10 Nonlinear systems in control theory 34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations 70K30 Nonlinear resonances for nonlinear problems in mechanics
##### Keywords:
auto-oscillations; quenching; control system; nonlinear system