Historical Remarks on Andronov-Witt’s Jump Postulate and its Generalization to Nonlinear Reciprocal Circuits

Mathis, Wolfgang; Thiessen, Tina; Popp, M.

doi:10.1007/978-3-319-08672-9_11

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2021

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“…This statement, known as the Andronov-Witt theorem [1,3,4], is also extended to the case of irregular linearization by exploiting a moving Poincaré section in [5] and autonomous impulsive systems in [7]. Further comments on the contribution of Andronov and Witt to the theory of nonlinear oscillations are presented in [6].…”

Section: Introductionmentioning

confidence: 99%

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

Zuyev

Benner

Seidel‐Morgenstern

2021

Proc Appl Math & Mech

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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.

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