Relations between Bohl exponents and general exponent of discrete linear time-varying systems

ABSTRACT

In the paper, properties of the upper Bohl exponents and senior upper general exponent of discrete linear time-varying systems are investigated. The relation of these exponents to uniform exponential stability is discussed. Moreover, an example of system, which is not uniformly exponentially stable but each trajectory tends uniformly and exponentially to zero is provided.

KEYWORDS:

• Uniform exponential stability
• discrete linear time-varying systems
• Bohl exponents
• senior upper general exponent
• Lyapunov exponents

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 34-D08
• 37-C75
• 39-A30

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Artur Babiarz http://orcid.org/0000-0002-7841-7151

Adam Czornik http://orcid.org/0000-0003-2492-4155

Michał Niezabitowski http://orcid.org/0000-0003-4553-5351

Additional information

Funding

The work of the first and second author was done as part of the project funded by the National Science Centre in Poland granted according to decision DEC-2015/19/D/ST7/03679 and DEC-2017/25/B/ST7/02888, respectively. The work of the last author was supported by the Polish National Agency for Academic Exchange according to decision PPN/BEK/2018/1/00312/DEC/1.