On participation factors for linear systems

Participation factors are nondimensional scalars that measure the interaction between the modes and the state variables of a linear system. Since their introduction by Verghese, Pérez-Arriaga and Schweppe, participation factors 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 of these definitions is to achieve a conceptual framework that doesn’t hinge on any particular choice of initial condition. The initial condition is modeled as an uncertain quantity, which can be viewed either in a set-valued or a probabilistic setting. If the initial condition uncertainty obeys a symmetry condition, the new definitions are found to reduce to the original definition of participation factors.