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Upper Bounds on Peaks in Discrete-Time Linear Systems

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Abstract

Trajectories of stable linear systems with nonzero initial conditions are known to deviate considerably from the zero equilibrium point at finite time instances. In the paper we analyze transients in discrete-time linear systems and provide upper bounds on deviations (peaks) via use of linear matrix inequalities. An approach to peak-minimizing feedback design is also proposed. An analysis of peak effects for norms of powers of Schur stable matrices is presented and a robust version of the problem is considered. The theory is illustrated by numerical examples.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology, Dolgoprudnyi, Russia

    U. M. Ahiyevich

  2. Skolkovo Institute of Science and Technology, Moscow region, Russia

    S. E. Parsegov

  3. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    S. E. Parsegov & P. S. Shcherbakov

  4. Institute for Systems Analysis, Russian Academy of Sciences, Moscow, Russia

    P. S. Shcherbakov

Authors
  1. U. M. Ahiyevich
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  2. S. E. Parsegov
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  3. P. S. Shcherbakov
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Corresponding author

Correspondence to U. M. Ahiyevich.

Additional information

Original Russian Text © V.N. Ahiyevichh, S.E. Parsegov, P.S. Shcherbakov, 2018, published in Avtomatika i Telemekhanika, 2018, No. 11, pp. 32–46.

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Ahiyevich, U.M., Parsegov, S.E. & Shcherbakov, P.S. Upper Bounds on Peaks in Discrete-Time Linear Systems. Autom Remote Control 79, 1976–1988 (2018). https://doi.org/10.1134/S0005117918110036

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