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Incremental nonlinear stability analysis of stochastic systems perturbed by Lévy noise

Han, SooJean and Chung, Soon-Jo (2022) Incremental nonlinear stability analysis of stochastic systems perturbed by Lévy noise. International Journal of Robust and Nonlinear Control, 32 (12). pp. 7174-7201. ISSN 1049-8923. doi:10.1002/rnc.6216.

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We present a theoretical framework for characterizing incremental stability of nonlinear stochastic systems perturbed by either compound Poisson shot noise or finite-measure Lévy noise. For each noise type, we compare trajectories of the perturbed system with distinct noise sample paths against trajectories of the nominal, unperturbed system. We show that for a finite number of jumps arising from the noise process, the mean-squared error between the trajectories exponentially converge toward a bounded error ball across a finite interval of time under practical boundedness assumptions. The convergence rate for shot noise systems is the same as the exponentially stable nominal system, but with a tradeoff between the parameters of the shot noise process and the size of the error ball. The convergence rate and the error ball for the Lévy noise system are shown to be nearly direct sums of the respective quantities for the shot and white noise systems separately, a result which is analogous to the Lévy–Khintchine theorem. We demonstrate both empirical and analytical computation of the error ball using several numerical examples, and illustrate how varying the parameters of the system affect the tightness of the bound.

Item Type:Article
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URLURL TypeDescription Paper
Chung, Soon-Jo0000-0002-6657-3907
Alternate Title:Incremental Nonlinear Stability Analysis for Stochastic Systems Perturbed by Lévy Noise
Additional Information:© 2022 John Wiley & Sons. Issue Online: 13 July 2022; Version of Record online: 06 June 2022; Manuscript accepted: 06 May 2022; Manuscript revised: 09 April 2022; Manuscript received: 22 October 2021. The authors would like to thank John C. Doyle for the insights he provided as motivation for this work. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1745301. DATA AVAILABILITY STATEMENT. Data sharing is not necessarily applicable to this article since no new data was generated for this study. However, the codes which were used to conduct the numerical studies in Section 5 are available from the corresponding author upon reasonable request. The authors declare no potential conflict of interests.
Funding AgencyGrant Number
NSF Graduate Research FellowshipDGE-1745301
Subject Keywords:nonlinear stochastic systems; Poisson processes; robust stability analysis; stability criteria; stochastic processes
Issue or Number:12
Record Number:CaltechAUTHORS:20210510-141340828
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Official Citation:Han, SJ, Chung, S-J. Incremental nonlinear stability analysis of stochastic systems perturbed by Lévy noise. Int J Robust Nonlinear Control. 2022; 32 (12): 7174-7201. doi:10.1002/rnc.6216
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:109050
Deposited By: George Porter
Deposited On:10 May 2021 21:36
Last Modified:03 Aug 2022 18:37

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