Unimodal self-oscillations and their sign-symmetry for discrete-time relay feedback systems with dead zone
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911519916163072 |
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| author | Tong, Kang Grussler, Christian Chong, Michelle S. |
| author_facet | Tong, Kang Grussler, Christian Chong, Michelle S. |
| contents | This paper characterizes self-oscillations in discrete-time linear time-invariant (LTI) relay feedback systems with nonnegative dead zone. Specifically, we aim to establish existence criteria for unimodal self-oscillations, defined as periodic solutions where the output exhibits a single-peaked period. Assuming that the linear part of system is stable, with a strictly monotonically decreasing impulse response on its infinite support, we propose a novel analytical framework based on the theory of total positivity to address this problem. We demonstrate that unimodal self-oscillations subject to mild variation-based constraints exist only if the number of positive and negative values of the system's loop gain coincides within a given strictly positive period, i.e., the self-oscillation is sign-symmetric. Building upon these findings, we derive conditions for the existence of such self-oscillations, establish tight bounds on their periods, and address the question of their uniqueness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_15393 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Unimodal self-oscillations and their sign-symmetry for discrete-time relay feedback systems with dead zone Tong, Kang Grussler, Christian Chong, Michelle S. Optimization and Control Systems and Control Dynamical Systems 93C10, 39A21, 93B52, 37C25, 37C79 This paper characterizes self-oscillations in discrete-time linear time-invariant (LTI) relay feedback systems with nonnegative dead zone. Specifically, we aim to establish existence criteria for unimodal self-oscillations, defined as periodic solutions where the output exhibits a single-peaked period. Assuming that the linear part of system is stable, with a strictly monotonically decreasing impulse response on its infinite support, we propose a novel analytical framework based on the theory of total positivity to address this problem. We demonstrate that unimodal self-oscillations subject to mild variation-based constraints exist only if the number of positive and negative values of the system's loop gain coincides within a given strictly positive period, i.e., the self-oscillation is sign-symmetric. Building upon these findings, we derive conditions for the existence of such self-oscillations, establish tight bounds on their periods, and address the question of their uniqueness. |
| title | Unimodal self-oscillations and their sign-symmetry for discrete-time relay feedback systems with dead zone |
| topic | Optimization and Control Systems and Control Dynamical Systems 93C10, 39A21, 93B52, 37C25, 37C79 |
| url | https://arxiv.org/abs/2603.15393 |