Читать книгу PID Passivity-Based Control of Nonlinear Systems with Applications - Romeo Ortega - Страница 29

Consider the system with passive output 2.3 and a dynamic extension

where . Define the overall system dynamics as , where . A necessary condition for the existence of a constant solution to the equilibrium equation

is that the system does not suffer from the dissipation obstacle, i.e., 2.4 holds.

Proof. The proof is established as follows:

Now

On the other hand,

The proof is completed substituting the last identity in the one above.