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EXPONENTIAL STABILITY OF IMPLICIT DIFFERENCE EQUATIONS

Annotation

An implicit difference equation in an arbitrary metric space is considered. The concept of partial exponential stability is introduced. The stability conditions are found. The study is based on the results about covering mapping of metric spaces.

Keywords

implicit difference equation; stability of equilibrium position; exponential stability; covering mapping of metric spaces

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UDC

517.962.24 + 517.929.9

Pages

1156-1160

References

1. Zaytsev V.A. Obobshchenie teoremy Dzhardzhevicha–Kuinna i stabilizatsiya bilineynykh upravlyaemykh sistem s periodicheskimi koeffitsientami. I // Differentsial'nye uravneniya. 2013. T. 49. №1. S. 101–110. 2. Zaytsev V.A. Obobshchenie teoremy Dzhardzhevicha–Kuinna i stabilizatsiya bilineynykh upravlyaemykh sistem s periodicheskimi koeffitsientami. II // Differentsial'nye uravneniya. 2013. T. 49. № 3. S. 348–357. 3. Zaitsev V.A. Global asymptotic stabilization of bilinear control systems with periodic coefficients // Vestnik Udmurtskogo universiteta. Matematika. Mekhanika. Komp'yuternye nauki. 2012. Vyp. 2. S. 17–27. 4. Zaytsev V.A. Stabilizatsiya affinnykh upravlyaemykh sistem s periodicheskimi koeffitsientami // Differentsial'nye uravneniya. 2013. T. 49. № 12. S. 1664–1672. 5. Zaitsev V.A. Global asymptotic stabilization of affine periodic systems by damping control // IFAC Papers Online. 5th IFAC International Workshop on Periodic Control Systems. 2013. Vol. 5. Part 1. P. 166–170.

Received

2015-06-12

Section of issue

Scientific articles

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