Automation and Remote Control

, Volume 80, Issue 9, pp 1681–1693 | Cite as

Synthesis of Anisotropic Suboptimal PID Controller for Linear Discrete Time-Invariant System with Scalar Control Input and Measured Output

  • M. M. TchaikovskyEmail author
  • V. N. TiminEmail author
  • A. P. Kurdyukov
Topical Issue


This paper considers the problem of synthesis of a proportional-integral-derivative control law (PID controller) for a linear discrete time-invariant system with scalar control input and measured output operating under influence of the stochastic disturbances with uncertainty described in terms of the mean anisotropy. The closed-loop system abilities to attenuate the disturbances are quantitatively characterized by the anisotropic norm. Sufficient existence conditions for the anisotropic suboptimal controller that stabilizes the closed-loop system and guarantees that its anisotropic norm is strictly bounded by a given threshold value are derived.


PID controller mean anisotropy norm suboptimal control convex optimization 


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This work is partially supported by Program 15 of Division of Power Engineering, MachineBuilding, Mechanics and Control Processes of Russian Academy of Sciences and Russian Foundation for Basic Research, project no. 17-08-00185.


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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Academician Pilyugin CenterMoscowRussia
  2. 2.Trapeznikov Institute of Control SciencesRussian Academy of SciencesMoscowRussia

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