A New Interpretation of Order-Changes in Terms of Mode-Shifts in a Descriptor System

Shin Kawai and Noriyuki Hori


Modelling and Simulation, Order Changes, Exponential/Static/Impulsive Modes, Descriptor Form


A descriptor form that is convenient to investigate the effects of order-changes caused in a certain manner is proposed. Using this form, such effects are given new interpretations in terms of associated shifts of modes among the exponential, the static, and the impulsive modes of a descriptor system. It is shown that when the order is reduced, a dynamic mode changes to a stat-ic/impulsive mode that is disconnected to the output and is impulse-unobservable. Such a static/impulsive mode can be interpreted as a reminiscence of a dynamic mode that disappeared from but remained within the system expression after the order reduction. While this interpretation is obtained under a particular rule of or-der-changes, the basic insights obtained should be use-ful in analysing and designing control systems that can involve, directly or indirectly, order changes.

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