Informatica

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.

The sequential nonlinear mapping is suitable for sequential detection of states of dynamic systems (Montvilas, 1999a). In addition, it can indicate the undesirable states and even the damages of dynamic systems. The last is complicated when the damage is caused by a small changing of respective parameter describing the state. In the paper the problem of nonlinear mapping to be sensitive for the small changing of parameters and the problem related with dimensionality of parameters are solved by using a special pre-processing of data. Examples are given.

This paper considers the control problem of a class of linear hereditary systems subjected to a nonlinear (perhaps) time-varying controller. The absolute stability for a class of nonlinear time-varying controllers are investigated. Sufficient conditions for absolute stability and hyperstability are given.