Input-to-state stability meets small-gain theory
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929400284446720 |
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| author | Mironchenko, Andrii |
| author_facet | Mironchenko, Andrii |
| contents | Input-to-state stability (ISS) unifies global asymptotic stability with respect to variations of initial conditions with robustness with respect to external disturbances. First, we present Lyapunov characterizations for input-to-state stability as well as ISS superpositions theorems showing relations of ISS to other robust stability properties. Next, we present one of the characteristic applications of the ISS framework - the design of event-based control schemes for the stabilization of nonlinear systems. In the second half of the paper, we focus on small-gain theorems for stability analysis of finite and infinite networks with input-to-state stable components. First, we present a classical small-gain theorem in terms of trajectories for the feedback interconnection of 2 nonlinear systems. Finally, a recent Lyapunov-based small-gain result for a network with infinitely many ISS components is shown. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17909 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Input-to-state stability meets small-gain theory Mironchenko, Andrii Optimization and Control Systems and Control Dynamical Systems Input-to-state stability (ISS) unifies global asymptotic stability with respect to variations of initial conditions with robustness with respect to external disturbances. First, we present Lyapunov characterizations for input-to-state stability as well as ISS superpositions theorems showing relations of ISS to other robust stability properties. Next, we present one of the characteristic applications of the ISS framework - the design of event-based control schemes for the stabilization of nonlinear systems. In the second half of the paper, we focus on small-gain theorems for stability analysis of finite and infinite networks with input-to-state stable components. First, we present a classical small-gain theorem in terms of trajectories for the feedback interconnection of 2 nonlinear systems. Finally, a recent Lyapunov-based small-gain result for a network with infinitely many ISS components is shown. |
| title | Input-to-state stability meets small-gain theory |
| topic | Optimization and Control Systems and Control Dynamical Systems |
| url | https://arxiv.org/abs/2406.17909 |