About Some Controllability Properties of Linear Discrete-Time Systems in Probabilistic Metric Spaces

Article type: Research Article

Authors: De La Sen, Manuel

Affiliations: Institute of Research and Development of Processes IIDP, Faculty of Science and Technology, University of the Basque Country, PO Box 644 Bilbao, Barrio Sarriena, 48940 Leioa (Bizkaia), Spain. E-mail: manuel.delasen@ehu.es

Abstract: This paper investigates in a formal context some fundamental controllability properties “from” and “to” the origin of probabilistic discrete-time dynamic systems as well as their uniform versions and complete controllability in a class of probabilistic metric spaces or probabilistic normed spaces, in particular, in probabilistic Menger spaces. Some related approximate probabilistic controllability properties are also investigated for the case when a nominal controllable system is subject to either parametrical perturbations or unmodelled dynamics. In this context, the approximate controllability of a perturbed system is a robustness-type approximate controllability provided that the nominal system is controllable. Some illustrative examples are also given.

Keywords: probabilistic metric spaces, Menger spaces, controllabillity, dynamic systems

Journal: Informatica, vol. 27, no. 3, pp. 503-526, 2016