Necessary and sufficient conditions for quenching auto-oscillations in nonlinear systems (Q1377953)

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.