Determination of Vertices and Edges in a Parametric Polytope to Analyze Root Indices of Robust Control Quality

  • Sergey Gayvoronskiy
  • Tatiana Ezangina
  • Ivan KhozhaevEmail author
  • Viktor Kazmin
Reseach Article


The research deals with the methodology intended to root robust quality indices in the interval control system, the parameters of which are affinely included in the coefficients of a characteristic polynomial. To determine the root quality indices we propose to depict on the root plane not all edges of the interval parametric polytope (as the edge theorem says), but its particular vertex-edge route. In order to define this route we need to know the angle sequence at which the edge branches depart from any integrated pole on the allocation area. It is revealed that the edge branches can integrate into the route both fully or partially due to intersection with other branches. The conditions which determine the intersection of one-face edge images have been proven. It is shown that the root quality indices can be determined by its ends or by any other internal point depending on a type of edge branch. The conditions which allow determining the edge branch type have been identified. On the basis of these studies we developed the algorithm intended to construct a boundary vertex-edge route on the polytope with the interval parameters of the system. As an illustration of how the algorithm can be implemented, we determined and introduced the root indices reflecting the robust quality of the system used to stabilize the position of an underwater charging station for autonomous unmanned vehicles.


Robust control parametric uncertainty parametric polytope interval parameters system analysis 


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This work was supported by the Ministry of Education and Science of the Russian Federation (No. 2.3649. 2017/PCh).


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Copyright information

© Institute of Automation, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Computer Science and RoboticsNational Research Tomsk Polytechnic UniversityTomskRussia

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