Nonquadratic global asymptotic stability certificates for saturated linear feedbacks
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912818053251072 |
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| author | Cristofaro, Andrea Zaccarian, Luca |
| author_facet | Cristofaro, Andrea Zaccarian, Luca |
| contents | We establish sufficient conditions for positive (semi-)definiteness, with or without radial unboundedness, for nonquadratic Lyapunov function constructed as sign-indefinite quadratic forms involving the state and the deadzone of a suitable input. We then use these conditions to build weak nonquadratic Lyapunov functions establishing global asymptotic stability of linear systems in feedback through a saturation, leveraging invariance principles. Our results are shown to be non-conservative (necessary and sufficient) for a family of well known prototypical examples of linear SISO feedbacks that are not globally exponentially stabilizable (the so-called ANCBI plants). Our multi-input extension leads to convex stability analysis tests, formulated as linear matrix inequalities that are applicable to ANCBI non-globally-exponentially-stabilizable plants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07431 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nonquadratic global asymptotic stability certificates for saturated linear feedbacks Cristofaro, Andrea Zaccarian, Luca Optimization and Control Systems and Control We establish sufficient conditions for positive (semi-)definiteness, with or without radial unboundedness, for nonquadratic Lyapunov function constructed as sign-indefinite quadratic forms involving the state and the deadzone of a suitable input. We then use these conditions to build weak nonquadratic Lyapunov functions establishing global asymptotic stability of linear systems in feedback through a saturation, leveraging invariance principles. Our results are shown to be non-conservative (necessary and sufficient) for a family of well known prototypical examples of linear SISO feedbacks that are not globally exponentially stabilizable (the so-called ANCBI plants). Our multi-input extension leads to convex stability analysis tests, formulated as linear matrix inequalities that are applicable to ANCBI non-globally-exponentially-stabilizable plants. |
| title | Nonquadratic global asymptotic stability certificates for saturated linear feedbacks |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2601.07431 |