Stabilization of linear time-varying reduced-order models: A feedback controller approach

Many of the commonly used methods in model-order reduction do not guarantee stability of the reduced-order model. This article extends the eigenvalue reassignment method of stabilization of linear time-invariant ROMs, to the more general case of linear time-varying systems. Through a postprocessing step, the ROM is controlled to ensure the stability while enhancing/maintaining its accuracy using a constrained nonlinear lease-square minimization problem. The controller and the input signals are defined at the algebraic level, using left and right singular vectors of the reduced system matrices. The choice provides a control on the upper bound of the growth of the energy of the reduced system. The optimization problem is applied to several time-invariant, time-periodic, and time-varying problems, and the reproductive and predictive capabilities of the proposed method, with respect to novel inputs and the system parameters, are evaluated.