scholarly journals Exponential dichotomies for linear discrete-time systems in Banach spaces

2012 ◽  
Vol 6 (1) ◽  
pp. 140-155 ◽  
Author(s):  
Ioan-Lucian Popa ◽  
Mihail Megan ◽  
Traian Ceauşu
Keyword(s):  
Banach Spaces ◽  
Discrete Time ◽  
Difference Equations ◽  
Linear Difference Equations ◽  
Exponential Dichotomies ◽  
Discrete Time Systems ◽  
Time Systems

In this paper we investigate some dichotomy concepts for linear difference equations in Banach spaces. Characterizations of these concepts are given. Some illustrating examples clarifies the relations between these concepts.

scholarly journals Nonuniform Exponential Trichotomy for Linear Discrete-Time Systems in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Xiao-qiu Song ◽  
Tian Yue ◽  
Dong-qing Li
Keyword(s):  
Exponential Stability ◽  
Banach Spaces ◽  
Discrete Time ◽  
Difference Equations ◽  
Exponential Dichotomy ◽  
Linear Difference Equations ◽  
Discrete Time Systems ◽  
Exponential Trichotomy ◽  
Time Systems

The aim of this paper is to give several characterizations for nonuniform exponential trichotomy properties of linear difference equations in Banach spaces. Well-known results for exponential stability and exponential dichotomy are extended to the case of nonuniform exponential trichotomy.

scholarly journals On (h,k)-Dichotomies for Nonautonomous Linear Difference Equations in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Mihai Gabriel Babuţia ◽  
Mihail Megan ◽  
Ioan-Lucian Popa
Keyword(s):  
Banach Spaces ◽  
Discrete Time ◽  
Difference Equations ◽  
Linear Difference Equations ◽  
Discrete Time Systems ◽  
Time Systems

This paper considers two general concepts of dichotomy for noninvertible and nonautonomous linear discrete-time systems in Banach spaces. These concepts use two types of dichotomy projections sequences (invariant and strongly invariant) and generalize some well-known dichotomy concepts (uniform, nonuniform, exponential, and polynomial). In the particular case of strongly invariant dichotomy projections, we present characterizations of these sequences and connections with other dichotomy concepts existent in the literature. Some illustrative examples clarify the implications between these concepts.

scholarly journals Nonuniform Exponential Dichotomies in Terms of Lyapunov Functions for Noninvertible Linear Discrete-Time Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Ioan-Lucian Popa ◽  
Mihail Megan ◽  
Traian Ceauşu
Keyword(s):  
Discrete Time ◽  
Lyapunov Functions ◽  
Exponential Dichotomies ◽  
Discrete Time Systems ◽  
Nonuniform Exponential Dichotomies ◽  
Time Systems

The aim of this paper is to give characterizations in terms of Lyapunov functions for nonuniform exponential dichotomies of nonautonomous and noninvertible discrete-time systems.

Observability of linear discrete-time systems of algebraic and difference equations

2017 ◽  
Vol 92 (2) ◽  
pp. 339-355 ◽  
Author(s):  
Lazaros Moysis ◽  
Nicholas Karampetakis ◽  
Efstathios Antoniou
Keyword(s):  
Discrete Time ◽  
Difference Equations ◽  
Discrete Time Systems ◽  
Time Systems

scholarly journals Nonuniform Polynomial Dichotomy for Noninvertible Linear Discrete-Time Systems in Banach Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Tian Yue
Keyword(s):  
Banach Spaces ◽  
Discrete Time ◽  
Lyapunov Functions ◽  
Discrete Time Systems ◽  
Time Systems

We study three polynomial dichotomy concepts for linear discrete-time systems in Banach spaces. Our main objective is to give characterizations in terms of Lyapunov functions for nonuniform polynomial dichotomy of nonautonomous and noninvertible linear discrete-time systems.

scholarly journals On Nonuniform Polynomial Trichotomy of Linear Discrete-Time Systems in Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Zhi-gang Li ◽  
Xiao-qiu Song ◽  
Xiu-li Yang
Keyword(s):  
Banach Spaces ◽  
Discrete Time ◽  
Lyapunov Functions ◽  
Discrete Time Systems ◽  
Time Systems

We study two nonuniform polynomial trichotomy concepts for linear discrete-time systems in Banach spaces. Our main objective is to give summation property for nonuniform polynomial trichotomies. As for applications we obtain characterization of these concepts in terms of Lyapunov functions.

scholarly journals Stability criteria for positive linear discrete-time systems

Positivity ◽  
2021 ◽  
Author(s):  
Jochen Glück ◽  
Andrii Mironchenko
Keyword(s):  
Banach Spaces ◽  
Discrete Time ◽  
Positive Cone ◽  
Stability Criteria ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Discrete Time Systems ◽  
Small Gain ◽  
Time Systems ◽  
Ordered Banach Spaces

AbstractWe prove new characterisations of exponential stability for positive linear discrete-time systems in ordered Banach spaces, in terms of small-gain conditions. Such conditions have played an important role in the finite-dimensional systems theory, but are relatively unexplored in the infinite-dimensional setting, yet. Our results are applicable to discrete-time systems in ordered Banach spaces that have a normal and generating positive cone. Moreover, we show that our stability criteria can be considerably simplified if the cone has non-empty interior or if the operator under consideration is quasi-compact. To place our results into context we include an overview of known stability criteria for linear (and not necessarily positive) operators and provide full proofs for several folklore characterizations from this domain.

On h-Trichotomy of Linear Discrete-Time Systems in Banach Spaces

2014 ◽  
Vol 39 ◽  
pp. 329-339 ◽  
Author(s):  
Ioan-Lucian Popa ◽  
◽  
Mihail Megan ◽  
Traian Ceausu ◽  
◽  
...  
Keyword(s):  
Banach Spaces ◽  
Discrete Time ◽  
Discrete Time Systems ◽  
Time Systems
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