On interconnections of “mixed” systems using classical stability theory

In this paper, we derive stability results for large-scale interconnections of “mixed” linear, time-invariant systems using classical Nyquist arguments. We compare our results with Moylan and Hill (1978) [8]. Our results indicate that, if one relaxes assumptions on the subsystems in an interconnection from assumptions of passivity or small gain to assumptions of “mixedness,” then the Moylan and Hill-like conditions on the interconnection matrix become more stringent. Finally, we explore a condition for the stability of large-scale, time-varying interconnections of strictly positive real systems. This condition mirrors the condition obtained in [8] for time-invariant interconnections and is thus an extension of this work.