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Input-to-state stability of soft-reset systems with nonlinear data

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Abstract

Input-to-state stability (ISS) is considered for a nonlinear “soft-reset” system with inputs. The latter is a system that approximates a hard-reset system, which is modeled as a hybrid system with inputs. In contrast, a soft-reset system is modeled as a differential inclusion with inputs. Lyapunov conditions on the hard-reset system are given that guarantee ISS for the soft-reset system. In turn, it is shown when global asymptotic stability for the origin of the zero-input reset system guarantees ISS for nonzero inputs. Examples are given to demonstrate the theory.

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Funding

This work was supported by the Air Force Office of Scientific Research under grant AFOSR FA9550-21-1-0452.

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  1. Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA, 93106-9560, USA

    Matina Baradaran Hosseini, Justin H. Le & Andrew R. Teel

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  1. Matina Baradaran Hosseini
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  2. Justin H. Le
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  3. Andrew R. Teel
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Correspondence to Andrew R. Teel.

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Baradaran Hosseini, M., Le, J.H. & Teel, A.R. Input-to-state stability of soft-reset systems with nonlinear data. Math. Control Signals Syst. 35, 523–540 (2023). https://doi.org/10.1007/s00498-023-00347-4

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