Two-sided time domain order reduction methods for linear control systems

Large scale control systems appear in many areas of applications so that the direct simulation and synthesis of such systems is extremely time-consuming. Model order reduction has become an essential tool to enable a fast numerical simulation in practice. In this paper, we investigate two-sided model reduction methods for linear systems in the time domain, which are in contrast to the current one-sided methods. Based on Chebyshev polynomials, the Chebyshev coefficients for the higher derivatives of system outputs are derived. With the aid of the specific structures of such Chebyshev coefficients, reduced models are produced in a two-sided projection framework, which preserve the information both of the time and the frequency domain simultaneously, thereby providing a superior approximation compared to the one produced by one-sided methods. The efficiency of our approach is verified by using a numerical example.