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State Estimation and Control for Linear Aperiodic Impulsive Systems with Uncertain Disturbances

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Abstract

The following problems are solved for systems of differential equations with periodic or aperiodic impulses, when uncertain disturbances are taken into account: estimating the set of solutions with initial data from a given ellipsoid in the form of an evolving invariant ellipsoid; the synthesis problem of continuous-impulse control, providing finite time boundedness of the original system with respect to given sets. Using the quadratic Lyapunov function with variable parameters, these problems are reduced to optimization problems with differential and difference linear matrix inequalities. The results are illustrated by the second order example.

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Funding

The work was supported by Russian Foundation for Basic Research (project no. 18-08-01045a).

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Authors and Affiliations

  1. Kazan National Research Technical University Named after A.N. Tupolev – KAI, 10 K. Marx str., 420111, Kazan, Russia

    A. I. Malikov

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  1. A. I. Malikov
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Correspondence to A. I. Malikov.

Additional information

Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 6, pp. 43–54.

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Malikov, A.I. State Estimation and Control for Linear Aperiodic Impulsive Systems with Uncertain Disturbances. Russ Math. 65, 36–46 (2021). https://doi.org/10.3103/S1066369X21060050

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  • DOI: https://doi.org/10.3103/S1066369X21060050

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