Time domain dimension reduction for discrete-time systems via low-rank approximate Gramians

Abstract

This paper considers the topic on model order reduction (MOR) based on approximate Gramians for discrete-time systems (DTSs), appearing in integrated circuits (ICs) and other engineering fields. The proposed approach is implemented by a balanced truncation framework, where the time domain controllability and observability Gramians are approximated by a low-rank decomposition, whose factors are constructed of Charlier polynomial expansion coefficients from linear equations instead of Lyapunov equations, which makes it more efficient and flexible. In avoid of the drawback that may lead to an unstable reduced-order model (ROM), a modified version of dominant subspace projection is employed to calculate a stability-preserving ROM. Finally, a numerical simulation on IC chips model is provided, where the results demonstrate the effectiveness of our algorithms in the views of time cost and accuracy.