A sufficient condition for stability of the calculation of parameters of aperiodic processes based on second order difference equations

The stability problem for the calculation of parameters of the second order damping aperiodic processes is considered. The numerical method of the second order aperiodic process parameters determination, based on iterative procedure of difference equation coefficients calculation, is described. The inequalities allowing to provide the stability of the difference equation according to the considering aperiodic process parameters limits of variation, known a priori, are obtained. The theorem on the sufficient condition of stability of the normal equations system under the solving of problem of difference equation coefficients mean-square estimation is formulated and proved. The obtained results have the great practical importance and can be used for the selection of discretization period of experimental curve, describing the second order observed aperiodic process in the system output.

aperiodic second order processes, difference equations, iterative procedure, mean-square approximation, stability of the second order difference equation