CLF based designs with robustness to dynamic input uncertainties

The problem of robust stabilization of nonlinear systems in the presence of input uncertainties is of great importance in practical implementation. St abilizing control laws may not be robust to this type of uncertainty, espec ially if cancellation of nonlinearities is used in the design. By exploitin g a connection between robustness and optimality, "domination redesign" of the control Lyapunov function (CLF) based Sontag's formula has been shown t o possess robustness to static and dynamic input uncertainties. In this pap er we provide a sufficient condition for the domination redesign to apply. This condition relies on properties of local homogeneous approximations of the system and of the CLF. We show that an inverse optimal control law may not exist when these conditions are violated and illustrate how these condi tions may guide the choice of a CLF which is suitable for domination redesi gn. (C) 1999 Elsevier Science B.V. All rights reserved.