## Monotone stability of nonlinear feedback systems.(English)Zbl 0776.93039

The authors give a generalization of the small-gain theorem for feedback systems. The central concept is called monotone stability which lies somewhere between input-output stability and finite gain stability. This concept is more natural than finite-gain stability in the context of nonlinear systems as the formulation allows for more general functional gain bounds than the affine form of the finite gain result. It is shown that monotone stability can be used for a large class of nonlinear systems.

### MSC:

 93C10 Nonlinear systems in control theory 93D15 Stabilization of systems by feedback

### Keywords:

small-gain theorem; monotone stability