Upper Bounds of the Deviations in Linear Dynamical System with Bounded Disturbances
Pages 1702 - 1710
Abstract
A practically significant effect of a surge occurrences in linear dynamical systems under nonzero initial conditions is explored. The linear dynamical system subjected to unknown-but-bounded exogenous disturbances is considered. Using the apparatus of linear matrix inequalities and the invariant ellipsoids concept, the estimations of the upper bounds of the trajectories deviations are obtained, and an approach is suggested to the feedback design that minimizes the deviations. The efficacy of the approach proposed is illustrated on numerical examples.
References
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Polyak BT, Tremba AA, Khlebnikov MV, et al.Large Deviations in Linear Control Systems with Nonzero Initial ConditionsAutom. Remote Control201576no. 6957-9763374788
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Kvinto YaI and Khlebnikov MV Upper Estimate of Large Deviations in Linear Systems in Presence of Uncertainty Probl. Upravlen. 2018 no. 3 2-7
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Kvinto YaI and Khlebnikov MVUpper Bounds of Large Deviations in Linear Discrete-Time Systems: The Robust StatementUpravlen. Bolash. Sist.2019no. 7759-791420.93014
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Balandin DV and Kogan MM Sintez zakonov upravleniya na osnove lineinykh matrichnykh neravenstv (LMI-based Control System Design) 2007 Moscow Fizmatlit
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Polyak BT, Khlebnikov MV, and Shcherbakov PS Upravlenie lineinymi sistemami pri vneshnikh vozmushcheniyakh: tekhnika lineinykh matrichnykh neravenstv (Control of Linear Systems Subjected to Exogenous Distrubances: An LMI Approach) 2014 Moscow LENAND
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Boyd S, ElGhaoui L, Feron E, and Balakrishnan V Linear Matrix Inequalities in Systems and Control Theory 1994 Philadelphia SIAM
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Nazin SA, Polyak BT, and Topunov MVRejection of Bounded Exogenous Disturbances by the Method of Invariant EllipsoidsAutom. Remote Control200768no. 3467-4862304813
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Polyak BT, Topunov MV, and Shcherbakov PS The Invariant Ellipsoid Ideology in Robust Rejection of Exogenous Bounded Disturbances Stokhast. Optimiz. Informat. 2007 3 no. 1-1 51-84
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Khlebnikov MV, Polyak BT, and Kuntsevich VMOptimization of Linear Systems Subject to Bounded Exogenous Disturbances: The Invariant Ellipsoid TechniqueAutom. Remote Control201172no. 112227-22752919279
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© Pleiades Publishing, Inc. 2020.
Publisher
Plenum Press
United States
Publication History
Published: 01 September 2020
Accepted: 04 April 2019
Revision received: 27 January 2019
Received: 27 January 2019
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