I. Introduction
The key foundation in dissipativity theory of dynamical systems was presented by Willems in his seminal two-part paper [1], [2]. In particular, Willems [1] introduced definition of dissipativity for general dynamical systems in terms of an inequality involving a generalized system power input, or, supply rate, and a generalized energy function, or, storage function. Since Lyapunov functions can be viewed as generalization of energy functions for nonlinear dynamical systems, the notion of dissipativity, with appropriate storage functions and supply rates, can be used to construct Lyapunov functions for nonlinear feedback systems by appropriately combining storage functions for each subsystem. Even though the original work on dissipative dynamical systems was formulated in the state space setting describing the system dynamics in terms of continuous flows on appropriate manifolds, an input-output formulation for dissipative dynamical systems extending the notions of passivity [3], nonexpansivity [3], and conicity [3], [4] was presented in [5], [6], [7]. More recently, the notion of dissipativity theory was generalized in [8] to formalize the concepts of the nonlinear analog of strict positive realness and strict bounded realness. In particular, using exponentially weighted supply rates, the concept of exponential dissipativity was introduced in [8].