A note on passivity theory via Lyapunov like function

Passive theory has been paid much more attention since its debut for it has connection with physical properties and stability of the investigated systems. And, besides that, passive theory contributes for Lyapunov function further in part for its root in storage functions. On account of that, a new bridge between passivity and stability for non-autonomous systems is touched and built in this paper. After the detailed analysis of system storage function, it is cleared that energy storage function is Lyapunov-like function in essence. Behind the unseen passive nature, there exists a robust support, namely, Lyapunov-Like lemma, so as to come with the meaning of Lyapunov stability, naturally.