On the orbital stability of periodic trajectories of a class of discontinuous systems

This paper focuses on the stability analysis of periodic trajectories for non‐autonomous systems whose right‐hand sides are time‐periodic discontinuous functions. Such systems arise, in particular, in optimal control problems for nonlinear control systems with periodic bang‐bang inputs. We obtain su...

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Bibliographic Details
Published inProceedings in applied mathematics and mechanics Vol. 21; no. 1
Main Authors Zuyev, Alexander, Benner, Peter, Seidel-Morgenstern, Andreas
Format Journal Article
LanguageEnglish
Published Berlin Wiley-VCH GmbH 01.12.2021
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Summary:This paper focuses on the stability analysis of periodic trajectories for non‐autonomous systems whose right‐hand sides are time‐periodic discontinuous functions. Such systems arise, in particular, in optimal control problems for nonlinear control systems with periodic bang‐bang inputs. We obtain sufficient orbital stability conditions of the Andronov–Witt type for this class of systems. The proposed stability conditions are applied to the analysis of periodic extremal trajectories of the controlled nonlinear chemical reaction model.
ISSN:1617-7061
1617-7061
DOI:10.1002/pamm.202100222