[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14403/jcms.2020.33.2.237

ASYMPTOTIC STABILITY OF NON-AUTONOMOUS UPPER TRIANGULAR SYSTEMS AND A GENERALIZATION OF LEVINSON'S THEOREM

Lee, Min-Gi (Department of Mathematics Kyungpook National University)

Publication Information

Journal of the Chungcheong Mathematical Society / v.33, no.2, 2020 , pp. 237-253 More about this Journal

Abstract

This article studies asymptotic stability of non-auto nomous linear systems with time-dependent coefficient matrices {A(t)}_t∈ℝ. The classical theorem of Levinson has been widely used to science and engineering non-autonomous systems, but systems with defective eigenvalues could not be covered because such a family does not allow continuous diagonalization. We study systems where the family allows to have upper triangulation and to have defective eigenvalues. In addition to the wider applicability, working with upper triangular matrices in place of Jordan form matrices offers more flexibility. We interpret our and earlier works including Levinson's theorem from the perspective of invariant manifold theory.

Keywords

asymptotic stability; non-autonomous system; Levinson's Theorem;

Citations & Related Records

Reference

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