Compositional small-gain and small-phase stability analysis

Abstract

We adapt the small-gain and small-phase stability analysis to systems composed of MIMO LTI subsystems via an iteration of the series, parallel, and feedback interconnections. Based on a certain set of parameters (including the phase sector and the Crawford number) of the subsystems, we bound the same set of parameters of each consecutive interconnection. This is called "composition of bounds." Composing the gains of subsystems in the same manner enables the small-gain-or-phase analysis of fairly complex systems. The method is illustrated with two examples that are not tractable by the classical small-phase analysis, and one other example that nevertheless benefits from the compositional approach.