Abstract
The aim of this paper is to investigate stability and sensitivity of the observability variable in linear control systems, (LCS) for short. We first present two results of Hölder continuity in the abstract framework of the ordinary differential equation initial-value problem x′(t) = f(t,x(t)),x(t 0) = x 0. Afterwards, we apply our results to automatic systems, providing henceforth the sharpest bounds for the parametric input-output relation in LCS.
Similar content being viewed by others
References
Ait Mansour, M., Malaoui, A., Thibault, L.: Sensitivity for the Cauchy-Lipschitz problem: Application to lines of transmission, in preparation
Luenberger D.G. (1967). Canonical forms for linear multivariable systems. IEEE Trans. Automat. Control AC-12: 290–293
Guerre et, S., Postel, M.: Méthodes d’approximations, équations différentielles, applications Scilab, Mathématiques à l’université, collection dirigée par Charles-Michel Marle et Phylippe Pilibossian, Niveau L3, ellipses, Paris (2003)
Pang, J-S., Stewart, D.: Differential variational inequalities, Math. Programming, Serie A (2005) doi: 10.1007/s10107-006-0052-x
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mansour, M.A. On the perturbation of the observability equation in linear control systems. J Glob Optim 40, 169–174 (2008). https://doi.org/10.1007/s10898-007-9186-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10898-007-9186-5