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Acta Mathematica Vietnamica

On Structured Distance to Uncontrollability of General Linear Retarded Systems

icon-email Nguyen Khoa Son , Nguyen Thi Hong

Abstract

In this paper, we study the robustness of controllability in the state space Mp=Kn×Lp([h,0],Kn), 1<p<, or retarded systems described by linear functional differential equations (FDE) of the form x˙(t)=A0x(t)+h0d[η(θ)]x(t+θ)+B0u(t),x(t)Kn, 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 A0,η,B0 are subjected to structured perturbations. An example is provided to illustrate the obtained results.