Structure‐Preserving Model Reduction Approach for Structured Index‐2 Descriptor‐Systems

ABSTRACT This article presents a balancing‐based algorithm for reducing the complexity of structured discrete‐time linear time‐invariant (DT‐LTI) index‐2 descriptor systems. The proposed algorithm involves projecting the index‐2 system onto a hidden manifold, which converts it into a generalized system. However, this causes the system to lose its sparsity and become dense, which is impractical for large‐scale systems. To overcome this issue, the authors enhance the Smith‐based iterative method for solving discrete‐time algebraic Lyapunov equations, which allow for balanced truncation without explicitly forming the dense system. The proposed algorithm is shown to be efficient and robust through numerical simulations.