On structured distance to uncontrollability of general linear retarded systems

Abstract

In this paper, we study the robustness of controllability in the state space Mₚ = Kⁿ x Lₚ ([-h, 0], Kⁿ), 1< p < ∞, for retarded systems described by linear functional differential equations (FDE) of the form x(t)=A₀x(t)+ ∫º₋h d[ɳ(θ)] x (t+θ)+Bou(t), x(t) € K", u (t) € Kᵐ, K = C, or R. Some formulas for estimating and computing the distance to uncontrollability of a controllable FDE system are obtained under the assumption that the system's matrices Aₒ, ɳ, Bₒ are subjected to structured perturbations. An example is provided to illustrate the obtained results.