Читать книгу PID Passivity-Based Control of Nonlinear Systems with Applications - Romeo Ortega - Страница 21

From Proposition 2.1, we have that, for all signals , the output . Under some additional assumptions, it also follows that . For instance, the latter property holds true, with , under the very weak assumption that there exists a steady‐state with and constants. Invoking Theorem A.2 it follows that convergence of the output to zero is also achieved if is passive with a positive definite (with respect to the origin) storage function and the output is zero‐state detectable. Also, we note that the use of passivity in the design can potentially produce, in some cases, slow responses that cannot be improved due to limited tuning parameters, see, for instance, Section 4.5.