The Stability Problem for a Dynamic System with the Assimilation of Observational Data

The problem of stability of a dynamic system defined by a system of differential equations to the perturbation of the initial data and with the data assimilation is considered. The assimilation of observational data is realized by the previously published author's method. The stability condition for this data assimilation method is formulated in the classical sense of Lyapunov, and the solution of the system is corrected using observational data for a given time interval. Necessary and sufficient conditions are proposed under which this system is stable as a function of the observed values. A possible numerical experiment to test and to apply this theory is discussed.