A Characterization of Integral Input-to-state Stability for Hybrid Systems with Memory
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911618406809600 |
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| author | Wang, Wenbang Li, Neng Ren, Wei |
| author_facet | Wang, Wenbang Li, Neng Ren, Wei |
| contents | This paper addresses characterizations of Integral Input-to-State Stability (iISS) for hybrid systems with memory. Based on the Krasovskii approach, a novel Lyapunov characterization of iISS is established to extend the hybrid system theory to the time-delay case. In particular, we introduce the notions of dissipativity, detectability and storage functional to describe the iISS property from different perspectives. Under mild regularity and convexity assumptions, the equivalence relations among diverse stability descriptions are established, which lays a solid foundation for the control design. Finally, a numerical example is presented to illustrate the derived results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_21542 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Characterization of Integral Input-to-state Stability for Hybrid Systems with Memory Wang, Wenbang Li, Neng Ren, Wei Systems and Control 93C30, 93D05 This paper addresses characterizations of Integral Input-to-State Stability (iISS) for hybrid systems with memory. Based on the Krasovskii approach, a novel Lyapunov characterization of iISS is established to extend the hybrid system theory to the time-delay case. In particular, we introduce the notions of dissipativity, detectability and storage functional to describe the iISS property from different perspectives. Under mild regularity and convexity assumptions, the equivalence relations among diverse stability descriptions are established, which lays a solid foundation for the control design. Finally, a numerical example is presented to illustrate the derived results. |
| title | A Characterization of Integral Input-to-state Stability for Hybrid Systems with Memory |
| topic | Systems and Control 93C30, 93D05 |
| url | https://arxiv.org/abs/2604.21542 |