Relative Controllability of Neutral Differential Equations with a Delay

Abstract

The problem of relative controllability for linear systems of neutral differential equations with a delay is investigated. An equivalent condition of Kalman type is proved. All the control functions leading the system from an initial state to a desired arbitrary point are characterized in terms of shifted Legendre polynomials. Weakly nonlinear equations are discussed as well. The results obtained are illustrated with an example of competing biological systems.