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| Input-to-state stability and gain computation for networked control systems |
| QianqianCai1,MinyueFu2 |
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| (1 School of Automation, Guangdong University of Technology, Guangzhou 510006, Guangdong, China;2 School of System Design and Intelligent Manufacturing, Southern University of Science and Technology, Shenzhen 518055, Guangdong, China) |
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| 摘要: |
| This paper studies the stability problem for networked control systems. A general result, called network gain theorem, is
introduced to determine the input-to-state stability (ISS) for interconnected nonlinear systems. We show how this result
generalises the previously known small gain theorem and cyclic small gain theorem for ISS. For the case of linear networked
systems, a complete characterisation of the stability condition is provided, together with two distributed algorithms for
computing the network gain: the classical Jacobi iterations and a message-passing algorithm. For the case of nonlinear
networked systems, characterisation of the ISS condition can be done using M-functions, and Jacobi iterations can be used
to compute the network gain. |
| 关键词: Small gain theorem · Networked systems · Input-to-state stability · Robust stability · Distributed algorithm |
| DOI：https://doi.org/10.1007/s11768-023-00152-z |
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| 基金项目: |
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| Input-to-state stability and gain computation for networked control systems |
| Qianqian Cai1,Minyue Fu2 |
| (1 School of Automation, Guangdong University of Technology, Guangzhou 510006, Guangdong, China;2 School of System Design and Intelligent Manufacturing, Southern University of Science and Technology, Shenzhen 518055, Guangdong, China) |
| Abstract: |
| This paper studies the stability problem for networked control systems. A general result, called network gain theorem, is
introduced to determine the input-to-state stability (ISS) for interconnected nonlinear systems. We show how this result
generalises the previously known small gain theorem and cyclic small gain theorem for ISS. For the case of linear networked
systems, a complete characterisation of the stability condition is provided, together with two distributed algorithms for
computing the network gain: the classical Jacobi iterations and a message-passing algorithm. For the case of nonlinear
networked systems, characterisation of the ISS condition can be done using M-functions, and Jacobi iterations can be used
to compute the network gain. |
| Key words: Small gain theorem · Networked systems · Input-to-state stability · Robust stability · Distributed algorithm |
