Stability margins for multivariable linear time-invariant systems

In this paper, Singular Perturbation Margin (SPM) and Generalized Gain Margin (GGM) are used as the classical Phase Margin (PM) and Gain Margin (GM) like stability metrics for multivariable Linear Time-Invariant (LTI) systems established from the view of the singular perturbation and the regular perturbation, respectively. The bijective relationship between the SPM and PM of a multivariable LTI system is established as corresponding lemmas and theorems, which is a generalisation of the single input single output cases. The analysis process for SPM and GGM are provided here. All the theoretical results are shown by a two-input-two-output LTI system (a simple model of a two-body spacecraft with non-collocated sensors and actuators using position feedback) as an application example. Such results are one essential step towards the big map of establishing a set of both theoretically rigorous and physically meaningful stability margin metrics for NLTV systems.