Minimal Lethal Disturbance for Finite Dimensional Linear Systems

  • Abdes Samed Bernoussi
  • Mina Amharref
  • Mustapha Ouardouz
Part of the STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health book series (STEAM)


In this work we consider the problem of robust viability and viability radius for finite dimensional disturbed linear systems. The problem consists in the determination of the smallest disturbance f (in some disturbance set \({\mathcal {F}}\)), for which a given viable state z0 does not remains viable. We also consider the problem of the determination of the smallest disturbance f for which the viability set \(Viab_{{\mathcal {K}}}^{f}\) becomes empty; the smallest disturbance that makes all the \({\mathcal {K}}\)-viable states non viable, which we call the Minimal Lethal Disturbance (MLD). We give some characterizations of the viability radius and an illustration through some examples and connection with toxicity in biology.


Viability Viability radius Minimal lethal disturbance Robustness 



This work, presented in Honor of Prof. Norbert Hounkonnou for his 60th Birthday, is supported by MESRCFC and CNRST, Morocco under the projectPPR2/2016/79, OGI-Env.


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Abdes Samed Bernoussi
    • 1
  • Mina Amharref
    • 1
  • Mustapha Ouardouz
    • 2
  1. 1.GATTangierMorocco
  2. 2.MMC Team, Faculty of Sciences and TechniquesTangierMorocco

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