Interconnected systems for the Lyapunov’s linear operator equations in the Hilbert space
Oleksandr Pokutnyi,
Yevhen Panasenko,
Olena Polishchuk
Affiliations
Oleksandr Pokutnyi
Doctor of Physical and Mathematical Sciences, Department of differential equations and oscillations theory, Institute of mathematics of NAS of Ukraine, Tereshenkivska, 3, Kiev, 01024, Ukraine; Corresponding author.
Yevhen Panasenko
Candidate of Physical and Mathematical Sciences, Zaporizhzhia National University, 66 Zhukovsky street, Zaporizhzhia, 69600, Ukraine
Olena Polishchuk
Master of the second year, Faculty of Cybernetics and Computer Science, KNU Shevchenko, Akademika Hlushkova Ave, 4d, Kiev, 03680, Ukraine
This paper investigates a perturbed interconnected system for linear operator Lyapunov equations in Hilbert space. We establish solvability conditions for the operator system in cases where the generating system of equations does and does not have solutions. Solutions are sought in the form of a completely convergent series.
