Dynamic Dissipativity Theory for Stability of Nonlinear Feedback Dynamical Systems

A key result from dissipativity theory states that if two systems are dissipative with respect to compatible supply rates, then the feedback interconnection of the two systems is stable. In this paper, we extend this result to show that the stability result is valid even if the two systems are dynamic dissipative, where we define a system to be dynamic dissipative if the system cascaded with another (static or dynamic) operator is dissipative. The notion of dynamic dissipativity unifies and extends the classical dissipativity theory, Integral Quadratic Constraints (IQCs), and the multiplier theory method from the absolute stability theory.