Robust stabilizer synthesis for feedback systems containing time-varying nonlinear perturbations

A new circle criterion is developed to solve the robust stabilization problem of a feedback system with time-varying nonlinear perturbations which is different than previous results. Theorems presented in this note can be employed to treat systems with stable or unstable plants. The generally stabilizing controller, proposed by Youla et al. and the Schur function (Class
S
) will be employed to synthesize the robust stabilizer of a feedback system subjected to time-varying nonlinear perturbations.