Abstract
We consider an ensemble of trajectories generated by a linear differential equation subjected to disturbance and parameterized by the initial state. The scalar output of the system is the volume comprised by the states of the whole ensemble. Already the unperturbed dynamics is assumed to be unstable. In order to stabilize the system with unknown inputs in the ISS sense we design impulsive control actions based in the output signal and establish conditions under which the system possesses the ISS property under these impulsive actions.
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Acknowledgements
Ivan Atamas was supported by the DAAD via PhD scholarship. Sergey Dashkovskiy and Vitalii Slynko were supported by the German Research Foundation (DFG) via grant nr. DA 767/12-1.
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Ivan Atamas, Sergey Dashkovskiy and Vitalii Slynko contributed equally to this work.
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Atamas, I., Dashkovskiy, S. & Slynko, V. Impulsive Input-to-State Stabilization of an Ensemble. Set-Valued Var. Anal 31, 25 (2023). https://doi.org/10.1007/s11228-023-00688-x
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DOI: https://doi.org/10.1007/s11228-023-00688-x