Abstract:
Singular Perturbation Margin (SPM) and Generalized Gain Margin (GGM) are Phase Margin (PM) and Gain Margin (GM) like stability metrics. In this paper, the problem of SPM and GGM assessment for Linear Periodically Time-Varying (LPTV) systems is formulated, which provides a necessary step for the development of the theoretically based and practically efficient SPM and GGM analysis methodology for multivariable Nonlinear Time-Varying (NLTV) systems. Here, Chang transformation makes it possible to reduce the SPM analysis for Hill equations, which is essentially a stability problem of higher order LPTV systems due to the SPM gauge introduced dynamics, to second order LPTV systems. Based upon Floquet Theory, when different types of LPTV SPM gauges are designed, the SPM and GGM assessment methods for the second order and general order LPTV systems are established and stated by the corresponding lemmas, theorems and corollaries. The effectiveness of such methods are illustrated by an examples of a flexible inverted pendulum.
Keywords:
Stability margin, Singular perturbation, Regular perturbation, Linear periodically time-varying systems, Hill equation.
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