On Robustness Analysis in the Control of Nonlinear Systems

This paper deals with the class of nonlinear systems described by the equation M(q(t))q(t) = f(t) - N(q(t),q¿(t)) with f(t) a control input. We employ a simple method of control design which has two stages. First, a global linearization is performed to yield a decoupled controllable linear system. Then a controller is designed for this linear system. We provide a rigorous analysis of the effects of uncertain dynamics, which we study using robustness results in the time domain based on a Lyapunov equation and the total stability theorem. Using this approach we are able to give meaningful robustness bounds which justify assumptions that are currently made in the literature in an ad hoc fashion.