Abstract
We show by an example that small perturbations with respect to the convergence in measure of the coefficients A and B may affect the complete controllability of the linear control system \(\dot x = A(t)x + B(t)u(t)\), where x is the state and u is the control. This answers a question raised in Ref. 1.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
NASELLI RICCERI, O., A Theorem on the Controllability of Perturbed Linear Control Systems, Atti della Accademia Nazionale dei Lincei, Rendiconti delle Classe di Scienze Matematiche, Fisiche e Naturali, Vol. 83, pp. 89–91, 1989.
VILLANI, A., Complete Controllability of Perturbed Linear Control Systems, Revisited, Journal of Optimization Theory and Applications, Vol. 68, pp. 359–369, 1991.
CONTI, R., Contributions to Linear Control Theory, Journal of Differential Equations, Vol. 1, pp. 427–445, 1965.
CONTI, R., Linear Differential Equation and Control, Academic Press, London, England, 1967.
Rights and permissions
About this article
Cite this article
Sturiale, G. An Example on the Controllability of Perturbed Linear Control Systems. Journal of Optimization Theory and Applications 95, 723–728 (1997). https://doi.org/10.1023/A:1022642410188
Issue Date:
DOI: https://doi.org/10.1023/A:1022642410188