Ioan-Lucian Popa†, Traian Ceaușu‡, Larisa Elena Biriș§, Tongxing Li¶, Akbar Zadak
Abstract: This paper presents a new approach to formulating exponential behaviors like stability/instability for the linear time-varying systems and for the adjoint one. The classical concept of uniform exponential stability is generalized. Using this generalized concepts, some results
extending existing uniform exponential stability conditions for linear time-varying systems are derived. As special cases for these results, some conditions are derived for the adjoint system. A characterization of the generalized concepts in terms of Lyapunov sequences is also
given. Also, an example is included to further illustrate the connection with the classical concept of uniform exponential stability.
MSC: 93C55, 93D20
keywords: generalized exponential stability, generalized exponential instability, difference equation, (one side) linear time-varying discrete-time system.
DOI 10.56082/annalsarscimath.2020.1-2.256
† blucian.popa@uab.ro Department of Mathematics, ”1 Decembrie 1918” University of Alba Iulia, 510009-Alba Iulia, Romania
‡Faculty of Mathematics and Computer Science, West University of Timi¸soara, 300223- Timi¸soara, Romania
§Faculty of Mathematics and Computer Science, West University of Timi¸soara, 300223- Timi¸soara, Romania
¶School of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, P. R. China
kDepartment of Mathematics, University of Peshawar, Peshawar 25000, Pakistan
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 12 no 1-2, 2020
