NONUNIFORM POLYNOMIAL BEHAVIOR FOR LINEAR RANDOM ONE-SIDED DISCRETE-TIME SYSTEMS

Dedicated to the memory of Professor Mihail Megan

 

Oana Albescu†, Larisa Elena Biriș‡, Traian Ceaușu§, Nicolae Marian Seimeanu

Abstract: This paper investigates the concepts of nonuniform polynomial stability and instability for linear random one-sided discrete-time systems. We establish necessary and sufficient conditions for these properties and provide Lyapunov-type characterizations in terms of Lyapunov functions and Lyapunov norms.

Keywords: polynomial stability, polynomial instability, Lyapunov functions, Lyapunov norms.

MSC: 34D05, 93C55, 93D05.

DOI  10.56082/annalsarscimath.2026.3.105

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*Accepted for publication on March 17, 2026
†oana.albescu@unitbv.ro, Faculty of Mathematics and Computer Science, Transilvania University of Brasov, Romania
‡larisa.biris@e-uvt.ro, West University of Timisoara, Department of Mathematics, Timisoara, Romania
§traian.ceausu@e-uvt.ro, West University of Timisoara, Department of Mathematics, Timisoara, Romania
nicusei@yahoo.com, West University of Timisoara, Department of Mathematics, Timisoara, Romania

PUBLISHED in

Annals Academy of Romanian Scientists Series on Mathematics and Its Application,

Volume 18 no 3, 2026

ISSN ONLINE 2066 – 6594
ISSN PRINT 2066 – 5997