Small-gain conditions for exponential incremental stability in feedback interconnections

Abstract

We prove that under a small-gain condition, an interconnection of two globally incrementally exponentially stable systems inherits this property on any compact connected forward invariant set. It is also demonstrated that the interconnection inherits a weaker version of incremental exponential stability globally. An example illustrating the theoretical findings is given. The example also shows that the uniform negativity of the Jacobian is not necessary for incremental exponential stability.

Submitter to the 2025 64th IEEE Conference on Decision and Control (CDC)