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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.
93C10 Nonlinear systems in control theory
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
70K30 Nonlinear resonances for nonlinear problems in mechanics