Conditions for Scale-Based Decompositions in Singularly Perturbed Systems.

摘要

Singularly perturbed models of the form x(t) = A(epsilon)x(t), with A(epsilon) analytic at 0, nonsingular for epsilon Epsilon (0, epsilon 0) and singular at epsilon = 0, arise naturally in various problems of systems and control theory. Under a so-called multiple semi-simple null structure or MSSNS condition on A(epsilon), the eigenstructure of this matrix has a multiple scale property that allows the asymptotic eigenstructure of the matrix to be studied via reduced-order matrices associated with the separate scales. Under a stronger multiple semi-stability or MSST condition, this eigenstructure decomposition translates into a time-scale decomposition of the solution x(t) of the system. This paper is aimed at illuminating the MSSNS and MSST conditions.