On Participation Factors for Linear Systems

Participation factors are nondimensional scalars that measure the interaction betweenthe modes and the state variables of a linear system. Since their introduction byVerghese, P'erez-Arriaga and Schweppe, participationfactors have been used for analysis, order reduction and controller design in a variety of fields.In this paper, participation factors are revisited, resulting in new definitions. The aim ofthese definitions is to achieve a conceptual framework that doesn't hinge on anyparticular choice of initial condition. The initial condition is modeled as an uncertainquantity, which can be viewed either in a set-valued or a probabilistic setting.If the initial condition uncertainty obeys a symmetry condition, the new definitionsare found to reduce to the original definition of participation factors