Singular Perturbation Margin assessment of linear slowly time-varying systems

Singular Perturbation Margin (SPM) is a stability margin for Nonlinear (NL) systems established from the view of the singular perturbation (time-scale separation) parameter. This paper provides two SPM assessment methods: quantitative and qualitative methods for Linear Slowly Time-Varying (LSTV) systems. Quantitative method offers a more accurate estimated SPM than the qualitative method, while the latter is more insightful for the system analysis, and will be helpful for the SPM gauge design in the future. The effectiveness of the two methods is shown by a gain scheduling design example. The results in this paper could also be extended to nonlinear slowly time-varying systems by its linearization thereof.