Complexity of constrained switching for switched nonlinear systems with average dwell time: novel characterization

In so far developed theory of switched systems is largely based on assuming certain small but finite time interval termed average dwell time, which represents a constraint even when extremely small. Thus currently most of it appears characterized by some slow switching condition with average dwell time satisfying a certain lower bound. However, in cases of nonlinear systems, when the switching seizes to be slow there may well appear non-expected complexity phenomena of particularly different nature. A fast switching condition with average dwell time satisfying an upper bound is explored and established. Thus the theory is extended by shading new light on the underlying, switching caused, system complexities. A comparison analysis of these innovated characterizations via slightly different overview yielded new results on the transient behaviour of switched nonlinear systems, while preserving the system stability. The multiple-Lyapunov functions approach is the analysis framework.