Dynamic system characterization via Eigenvalue orbits

A new model-free approach for the description of general dynamical systems with unknown structure, order, and excitation is introduced. The approach i s based on the new concept of eigenvalue orbit, The eigenorbits are obtaine d by building an associated linear time-variant system through a matrix tha t relates the output measurements in a moving horizon window and viewing th e trajectories of its time-varying eigenvalues. How the eigenorbits may be computed from the measurements and used for the characterization of the ori ginal system is shown. The basic properties of the eigenorbits are presente d via a series of theorems for the case of a discrete-time, linear time-inv ariant system. A set of examples are included to illustrate these propertie s for more general classes of systems and to suggest some practical issues that can be drawn from the orbits.