TY  - JOUR
A1  - Dashkovskiy, Sergey
A1  - Slynko, Vitalii
T1  - Stability conditions for impulsive dynamical systems
JF  - Mathematics of Control, Signals, and Systems
N2  - In this work, we consider impulsive dynamical systems evolving on an infinite-dimensional space and subjected to external perturbations. We look for stability conditions that guarantee the input-to-state stability for such systems. Our new dwell-time conditions allow the situation, where both continuous and discrete dynamics can be unstable simultaneously. Lyapunov like methods are developed for this purpose. Illustrative finite and infinite dimensional examples are provided to demonstrate the application of the main results. These examples cannot be treated by any other published approach and demonstrate the effectiveness of our results.
KW  - lyapunov methods
KW  - stability
KW  - robustness
KW  - impulsive systems
KW  - infinite-dimensional systems
KW  - nonlinear systems
KW  - input-to-state stability
Y1  - 2022
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-268390
SN  - 1435-568X
VL  - 34
IS  - 1
ER  - 
TY  - JOUR
A1  - Dashkovskiy, Sergey
A1  - Kapustyan, Oleksiy
A1  - Schmid, Jochen
T1  - A local input-to-state stability result w.r.t. attractors of nonlinear reaction–diffusion equations
JF  - Mathematics of Control, Signals, and Systems
N2  - We establish the local input-to-state stability of a large class of disturbed nonlinear reaction–diffusion equations w.r.t. the global attractor of the respective undisturbed system.
KW  - local input-to-state stability
KW  - global attractor
KW  - lonlinear reaction-diffusion equations
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-281099
VL  - 32
IS  - 3
ER  -