On Strict Causality Conditions for Descriptor Systems With Unknown Inputs

This article investigates descriptor systems with unknown inputs that are not necessarily regular. The concept of strict causality is introduced to address the impulsive behavior of the system caused by unknown inputs and differentiating control inputs. By applying a decomposition, a reduced system is obtained, from which the unknown inputs are subsequently eliminated. Initially, conditions for causality and strict causality are presented in terms of the coefficient matrices of the reduced systems, both with and without unknown inputs. Using the strict causality of the reduced system, the strict causality condition of the original system is derived. The process to obtain these conditions is based on numerically stable orthogonal transformations. The proposed theory is elaborated with two numerical examples, demonstrating the practical relevance of the approach.