Observability Notions for CSVIU and Stability in Connection with Some Norms

This paper deals with some notions of observability coupled with corresponding notions of norm energy for a certain class of stochastic models. The class is devoted to systems subjected to a relevant degree of uncertainty, obtained from the concept that control and state variations increase uncertainties (CSVIU) in a poorly known system. The paper develops conditions under which finiteness of the norm connects with the stability of the system in an appropriate and similar stochastic sense. The rank test of the observability matrices ties these notions in an observability test, placing the analysis on the same foot of deterministic systems. Besides, the results here have the potential to establish useful connections for the stochastic norm problems presented here.