A new polynomial robust controller design for nonlinear uncertain systems

The problem of stabilizing a class of nonlinear uncertain systems is considered. The system possesses uncertainty which is time-varying; the uncertainty is unknown but lies within a prescribed set. No statistical information on the uncertainty is imposed. A new controller design which invokes a polynomial state dependent gain is proposed. The coefficients of the polynomial provide design flexibility. If the order of the polynomial is chosen high enough, then practical stability, is assured regardless of the choice of the coefficients. Two design methods, pole-placement and linear quadratic, are proposed for the coefficients