Further results on the existence of a continuous storage function for nonlinear dissipative systems

The problem of existence of continuous storage function for dissipative nonlinear systems is considered. It is shown that, if a nonlinear system is dissipative in the state x
∗
, then, under certain assumptions, a continuous storage function can be constructed on a set of points accessible from x
∗
by concatenation of a finite number of forward and backward motions of the system. Most of these assumptions are weaker than certain controllability-type properties and can be checked by the similar tests.