Operator methods of constructing matrix-valued Lyapunov functions
Ivan Atamas, Anatoliy A. Martynyuk, Vitalii Ivanovich Slyn'ko · 2024
We consider a two-component coupled system of differential equations with operator coefficients. In contrast to the well-known small-gain approach, we assume the presence of the exponential stability property of only one subsystem. We introduce a condition for the dominance of this subsystem, which allows us to prove new conditions for the exponential stability of a coupled system. An example of infinite networks is given. The results are compared with a small-gain approach based on the Lyapunov vector function.