On limit cycles in feedback polynomial systems

The problem of the existence and of the uncertainty of limit cycles in nonlinear feedback systems is examined. If approximate solution obtained using the describing function method is assumed to be known for a class of multiloop polynomial systems then sufficient conditions are derived to ensure in the neighborhood the existence of a true periodic solution and to evaluate its corresponding bounds. Numerical and graphical techniques are given in order to simplify the application of these results. In particular, for a special class of single-loop systems a procedure called the cone criterion is presented. A number of illustrative examples are provided