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Towards a comprehensive impossibility result for string stability

Arash Farnam 1 Alain Sarlette 2
2 QUANTIC - QUANTum Information Circuits
ENS Paris - École normale supérieure - Paris, MINES ParisTech - École nationale supérieure des mines de Paris, SU - Sorbonne Université, Inria de Paris
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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https://hal.inria.fr/hal-02394703
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Submitted on : Wednesday, December 4, 2019 - 9:50:40 PM
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Arash Farnam, Alain Sarlette. Towards a comprehensive impossibility result for string stability. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2019, ⟨10.1109/TAC.2019.2929967⟩. ⟨hal-02394703⟩

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