An Input-Output Approach to Incremental Feedback Stability

The well-posedness and incremental stability of feedback interconnections of nonlinear systems satisfying complementary incremental hard integral quadratic constraints (IQCs) are investigated. It is established that when these incremental IQCs are defined by indefinite static (i.e. matricial) multipliers, feedback well-posedness, which guarantees unique existence of causal solutions to the feedback equations, can be ascertained. We show that a well-posed feedback system is incrementally passive if and only if the open-loop systems are both incrementally passive. Furthermore, we derive an incremental feedback stability result based on incremental IQCs defined by dynamic multipliers and specialise them into incremental IQCs that characterise incremental passivity indices, where incremental passivity surplus in one system may be used to compensate for the deficiency in another from the perspective of establishing incremental feedback stability.