On participation factors for linear systems

Participation factors are nondimensional scalars that measure the interacti on between the modes and the state variables of a linear system. Since thei r introduction by Verghese, Perez-Arriaga and Schweppe, participation facto rs have been used for analysis, order reduction and controller design in a variety of fields. In this paper, participation factors are revisited, resu lting in new definitions. The aim of these definitions is to achieve a conc eptual framework that does not hinge on any particular choice of initial co ndition. The initial condition is modeled as an uncertain quantity, which c an be viewed either in a set-valued or a probabilistic setting. If the init ial condition uncertainty obeys a symmetry condition, the new definitions a re found to reduce to the original definition of participation factors. (C) 2000 Elsevier Science Ltd. All rights reserved.