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Finite-time stability for uncertain differential equations: a first investigation on a new class of multi-agent systems

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In this paper, we discuss a new kind of stability, that is, finite-time stability, for uncertain differential equations, by formalizing some properties. As a possible application, we define a new class of uncertain multi-agent systems, according to the Liu’s uncertainty theory, as a counterpart of stochastic multi-agent systems. We formalize the governing equations, driven by canonical process, which is a type of uncertain process with stationary and independent increments. The concept of finite-time consensus in the context of uncertainty theory is consequently derived. A numerical procedure to estimate the settling time is proposed. The case with proportional delay was also considered.

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Mrs Neda Gossili acknowledges the support from the Iranian Ministry of University and Research for spending six months of her PhD programme at the University of Salerno under the supervision of Dr Stefania Tomasiello. Mr Santiago Marín Mejía acknowledges the support from Maestría en Ingeniería de Sistemas y Computacion, Universidad Tecnologica de Pereira.

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Correspondence to S. Tomasiello.

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Tomasiello, S., Marín Mejía, S. & Gossili, N. Finite-time stability for uncertain differential equations: a first investigation on a new class of multi-agent systems. Soft Comput 24, 3275–3284 (2020). https://doi.org/10.1007/s00500-019-04086-0

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  • Uncertain differential equation
  • Liu’s process
  • Stability
  • Consensus
  • Fuzzy transform