Partial Stability of Nonlinear Dissipative Feedback Systems

Partially stable systems involve dynamical systems whose motion lie in a subspace of the state space resulting in system stability with respect to part of the system's states. In this paper, we develop partial stability theorems for nonlinear dissipative feedback systems. Specifically, by invoking additional structural constraints on the forward loop and feedback loop system storage functions, we develop feedback interconnection partial stability results for dissipative nonlinear dynamical systems. Our results provide extensions of the positivity and small gain theorems for guaranteeing partial stability of feedback interconnected systems.