Equilibrium-independent passivity: a new definition and implications

We extend the traditional notion of passivity to a forced system whose equilibrium is nontrivially dependent on the control input by defining equilibrium-independent passivity, a system property characterized by a dissipation inequality centered at an arbitrary equilibrium point. We also provide input/output tests to certify this property which can be performed analytically or empirically. An example from network stability analysis is presented which demonstrates the utility of this new definition. Finally, through a numerical example we show that equilibrium-independent passivity is less restrictive than incremental passivity.