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Journal Articles IEEE Transactions on Automatic Control Year : 2019

Towards a comprehensive impossibility result for string stability

Alain Sarlette
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Abstract

We provide a comprehensive impossibility result towards achieving string stability, i.e. keeping local relative errors in check with local controllers independently of the size of a chain of subsystems. We significantly extend existing results, from the LTI setting to any homogeneous controllers that can be nonlinear, time-varying, and locally communicating. We prove this impossibility for a set of definitions with various norm choices, including the L2-type standard and a BIBO type criterion. All results hold for a general discrete-time controller which should cover most applications.
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Dates and versions

hal-02394703 , version 1 (04-12-2019)

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Cite

Arash Farnam, Alain Sarlette. Towards a comprehensive impossibility result for string stability. IEEE Transactions on Automatic Control, 2019, 65 (4), pp.1652-1659. ⟨10.1109/TAC.2019.2929967⟩. ⟨hal-02394703⟩
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