Time Varying Covariance Equivalent Realizations

Non stationary generalizations of the Q-Markov Covariance equivalent system realizations from input-output experimental data are presented. For applications involving the stabilization of a mechanical system about a nominal trajectory, model identification of departure motion dynamics from data involves the realization of a time varying system. Specifying the covariance properties of the time varying departure motion dynamics model, this paper develops an approach to derive discrete time varying plant models directly from the data. The utility of using second order information in identification of system matrices comes from the fact that the state error covariance can be obtained simultaneously from the data. The model error characterization properties afforded by the larger degrees of design freedom provided by the time varying covariance equivalent system realizations are discussed in the paper.