Controllability and observability robustness of perturbed linear time invariant systems

The controllability and observability of a continuous linear time-invariant system (LTI) under perturbations are analyzed in this paper. Based on various mathematical tools, sufficient conditions to ensure controllability of LTI systems are presented. Besides, the perturbed system corresponds to a perturbation of the matrices, and the conditions that have been established are intimately linked to the structure of perturbed system. By duality, the robustness of observability is also ensured under suitable conditions.