The Structural Closure Property of Linear Time-Invariant Invertible Systems

This paper introduces and proves a novel proposition on the structural closure property of Linear Time-Invariant (LTI) invertible systems. Specifically, it demonstrates that systems composed by arbitrarily combining LTI invertible systems through cascade, parallel, and feedback configurations remain LTI invertible systems. Furthermore, a constructive approach is proposed to reinterpret systems governed by linear constant-coefficient differential equations, proving that under the assumption of causality, such systems are invertible. The theoretical contribution of this work enriches the understanding of invertibility in signal and system theory, while its practical value lies in providing structural support for the design and analysis of complex systems.