On nonlinear control of Euler-Lagrange systems: Disturbance attenuation properties

In this brief note we analyse the (local) disturbance attenuation properties of some asymptotically stabilizing nonlinear controllers for Euler-Lagrange systems reported in the literature. Our objective in this study is twofold: first, to compare the performance of these schemes from a perspective different from stabilizability; second, to quantify the basic tradeoff between robust stability and robust performance for these designs. We consider passivity-based and feedback linearization schemes developed for the ccntrol of DC-to-DC converters and rigid robots. For the DC-to-DC problem we show that for both controllers there exists a lower bound to the achievable attenuation level, i.e. a lower bound to the L2-gain of the closed loop operator from disturbance to regulated output, which is independent of the design parameters. Also, for the passivity based scheme we obtain an upper bound for the disturbance attenuation, which is insured provided we sacrifice the convergence rate. For rigid robots we show that both approaches yield arbitrarily good disturbance attenuation without compromising the convergence rate.