Search

In this paper, we consider model order reduction for bilinear systems with non-zero initial conditions. We discuss the choices of Gramians for both the homogeneous and the inhomogeneous parts of the system individually and prove how these Gramians characterise the respective dominant subspaces of each of the two subsystems. Proposing different, not necessarily structure preserving, reduced-order methods for each subsystem, we establish several strategies to reduce the dimension of the full system. For all these approaches, error bounds are shown depending on the truncated Hankel singular values of the subsystems. Besides the error analysis, stability is discussed. In particular, a focus is on a new criterion for the homogeneous subsystem guaranteeing the existence of the associated Gramians and an asymptotically stable realisation of the system. [ABSTRACT FROM AUTHOR]

This work focuses on the model order reduction problem for bilinear control systems with nonzero initial conditions. Based on the Volterra series analysis, the system response can be decomposed into three parts. The first two parts are the zero input response and zero initial condition response of the system. The third part describes the response which couples the effect of the nonzero initial condition and the nonzero input. The system corresponding to the third part is a bilinear control system with a special time-varying input coefficient matrix. We show that such a system is equivalent to a time-invariant bilinear control system, and conventional model reduction methods can be applied to reduce it. We propose to reduce each of the component responses independently and then combine them to approximate the full system response. This method is of high flexibility and shows promising results. [ABSTRACT FROM AUTHOR]