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GLOBAL LYAPUNOV REDUCIBILITY AND UNIFORM GLOBAL QUASI-ATTAINABILITY OF LINEAR DIFFERENTIAL SYSTEMS

Annotation

The paper considers the linear control system with locally integrable and integrally bounded coefficients. For her, we have defined the concept of uniform global quasi-attainability, and found that the presence of property of uniform global quasi-attainability of observe two-dimensional system a sufficient condition for its global Lyapunov reducible.

Keywords

global Lyapunov reducibility; uniform global controllability; uniform global attainability; uniform global quasi-attainability

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UDC

517.926+517.977

Pages

1187-1189

References

1. Bylov B.F., Vinograd R.E., Grobman D.M., Nemytskiy V.V. Teoriya pokazateley Lyapunova i ee prilozheniya k voprosam ustoychivosti. M.: Nauka, 1966. 2. Makarov E.K., Popova S.N. Upravlyaemost' asimptoticheskikh invariantov nestatsionarnykh lineynykh sistem. Minsk: Belarus. navuka, 2012. 3. Khorn R. Matrichnyy analiz. M.: Mir, 1989. 4. Tonkov E.L. Kriteriy ravnomernoy upravlyaemosti i stabilizatsiya lineynoy rekurrentnoy sistemy // Differents. uravneniya. 1979. T. 15. № 10. S. 1804–1813. 5. Kalman R.E. Contribution to the theory of optimal control // Boletin de la Sosiedad Matematika Mexicana, 1960. V. 5. № 1. P. 102–119. 6. Makarov E.K., Popova S.N. O global'noy upravlyaemosti polnoy sovokupnosti lyapunovskikh invariantov dvumernykh lineynykh sistem // Differents. uravneniya. 1999. T. 35. № 1. S. 97–106. 7.Popova S.N. Global'naya upravlyaemost' polnoy sovokupnosti lyapunovskikh invariantov periodicheskikh sistem // Differents. uravneniya. 2003. T. 39. № 12. S. 1627–1636. 8. Zaytsev V.A. Global'naya dostizhimost' i global'naya lyapunovskaya privodimost' dvumernykh i trekhmernykh lineynykh upravlyaemykh sistem s postoyannymi koeffitsientami // Vestnik Udmurtskogo un-ta. Seriya: Matematika. 2003. S. 31-62.

Received

2015-06-10

Section of issue

Scientific articles

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