Reduced‐order modeling methods for parametric bilinear systems via Walsh functions

Abstract This paper investigates model order reduction (MOR) methods for parametric bilinear systems using Walsh functions. First, the coefficient matrices are expanded via Taylor series to transform the system considered into a polynomial parametric system. The resulting system is then expanded using Walsh functions, where the bilinear terms are effectively handled, leading to a generalized Sylvester equation. Then, LU factorization combines with a hybrid iterative strategy to obtain the solution of the generalized Sylvester equation, which can significantly enhance the convergence rate of the generalized minimal residual method and reduce computational costs. Finally, orthogonal projection matrices are constructed from the obtained expansion coefficients to generate the parametric reduced‐order systems. Theoretical analysis shows that the reduced‐order systems can match the first several expansion coefficients of the output of the original system. Numerical experiments demonstrate the feasibility and effectiveness of the proposed methods.