On structured distance to uncontrollability of general linear retarded systems

Abstract

In this paper, we study the robustness of controllability in the state space Mρ = Kⁿ x Lρ ([ -h.0 ], Kⁿ), 1 < p < ∞, for retarded systems described by linear functional differential equations (FDE) of the form x(t) = Aox(t) + ∫°₋h d [ η (θ)] x (t + θ) + Bou(t), x(t) є Kⁿ, u(t) є 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 A₀, > η B₀ are subjected to structured perturbations. An example is provided to illustrate the obtained results.