Criterion for robustness of global asymptotic stability to external perturbations of linear time-varying systems

ABSTRACT

In this paper, we establish a new criterion for robustness of global asymptotic stability of zero solution of LTV system $\dot{x}=A(t)x$ in the presence of external perturbations (disturbances). To prove the result, logarithmic norm will be used under which the stability becomes a topological notion depending on the chosen vector norm in the state-space ${\mathbb{R}}^n.$

KEYWORDS:

• Linear time-varying system
• perturbation
• robust global asymptotic stability
• logarithmic norm

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

The research was supported by the project VEGA 1/0272/18: “Holistic approach of knowledge discovery from production data in compliance with Industry 4.0 concept” and by Research and Development Operational Program (ERDF) (European Regional Development Fund) [“University Scientific Park: Campus MTF STU - CAMBO”, grant number 26220220179].

Notes on contributors

R. Vrabel

Robert Vrabel received the Masters degree in Applied Mathematical Analysis in 1990 and Ph.D. in 1998 at the Slovak Academy of Sciences in Bratislava. At the present he is Associate Professor with the Institute of Applied Informatics, Automation and Mechatronics of the Faculty of Materials Science and Technology in Trnava, Slovak University of Technology in Bratislava, Slovakia. His current research interests include stability and control of linear and nonlinear systems, singular perturbations in dynamical systems and qualitative theory of ordinary differential equations generally.