Controllability and observability of formal perturbed linear time invariant systems

The controllability and the observability problems of formal perturbed linear time invariant systems (FPLTI) are studied in this paper. Thanks to numerous mathematical tools, a new controllability sufficient conditions for the FPLTI systems is derived. The study is presented using formal perturbation based on polynomials. By duality, the robustness of the observability for this kind of perturbed systems is also assured under appropriate conditions. Furthermore, the relationship between the optimal input energy of the formal perturbed system and that of the nominal system is established.