Читать книгу PID Passivity-Based Control of Nonlinear Systems with Applications - Romeo Ortega - Страница 23

As discussed earlier, it is necessary to ensure that the control law 2.1 can be computed without differentiation nor singularities. The latter may arise due to the presence of the derivative term . Clearly, this term can be added only when the output has relative degree one, that is, when .² But even for systems without a derivative action, a singularity may appear for systems with relative degree zero, that is with .

The required well‐posedness assumptions in both cases are stated in the lemma below, whose proof follows immediately computing the expressions of for the closed‐loop system. As will become clear below, the assumptions are technical only, and rather weak, but they are given for the sake of completeness.