Solutions of Stable Difference Equations Probably Experience Peak. Issue 2 (2020)

• Record Type: Journal Article
• Authors: Shcherbakov, Pavel; Dabbene, Fabrizio; Polyak, Boris
• Is Part Of: IFAC-PapersOnLine. Volume 53:Issue 2(2020)
• Page Start: 4762
• Page End: 4767
• Publication Date: 2020
• Subjects: linear difference equations -- stability -- nonzero initial conditions -- non-asymptotic behavior -- deviations -- probability; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2020.12.1001
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: From the literature, it is known that solutions of homogenous linear stable difference equations may experience large deviations, or peaks, from the nonzero initial conditions at finite time instants. In this paper we take a probabilistic standpoint to analyze these phenomena by assuming that both the initial conditions and the coefficients of the equation have random nature. Under these assumptions we find the probability for deviations to occur, which turns out very close to unity even for equations of low degree, which means that peak is typical. We also address other issues such as evaluation of the mean magnitude and maximum value of peak.