Cover Image

Criterion of the solvability of matrix equations of the Lyapunov type

By using the theory of generalized inverse operators, we establish a criterion of the solvability of the Lyapunov-type matrix equations AX - XB = D and X - AXB = D and investigate the structure of the set of their solutions.

Saved in:

Bibliographic Details
Date:	1998
Main Authors:	Boichuk, О. A., Krivosheya, S. A., Бойчук, О. А., Кривошея, С. А.
Format:	Article
Language:	Ukrainian English
Published:	Institute of Mathematics, NAS of Ukraine 1998
Online Access:	https://umj.imath.kiev.ua/index.php/umj/article/view/4851
Tags:	Add Tag No Tags, Be the first to tag this record!
Journal Title:	Ukrains’kyi Matematychnyi Zhurnal
Download file:

Institution

Ukrains’kyi Matematychnyi Zhurnal

Similar Items

A criterion of solvability of resonant equations and construction of their solutions
by: Boichuk, О. A., et al.
Published: (2026)

A criterion of solvability of resonant equations and construction of their solutions
by: O. A. Boichuk, et al.
Published: (2019)

Solvability criterion of linear boundary-value problems for integro-differential Fredholm equations with a degenerate kernel in Banach spaces
by: Boichuk , A. A., et al.
Published: (2020)

Construction of analogs of the Lyapunov equation for a matrix polynomial
by: Mazko, A. G., et al.
Published: (1995)

Bounded solutions of the nonlinear Lyapunov equation and homoclinic chaos
by: Boichuk, О. A., et al.
Published: (2019)

On the solvability of the Riccati matrix algebraic equation
by: Prokip, V. M., et al.
Published: (1994)

Solvability conditions for nonlinear matrix equations
by: S. M. Chuiko, et al.
Published: (2022)

Boundary-value problems for the Lyapunov equation. II
by: Boichuk, O., et al.
Published: (2024)

Boundary-value problems for the Lyapunov equation. І
by: Boichuk, O., et al.
Published: (2024)

Solvability criterion of linear boundary-value problems for integro-differential Fredholm equations with a degenerate kernel in Banach spaces
by: O. A. Boichuk, et al.
Published: (2020)

Solvability of integrodifferential equations with nondegenerate kernel in Hilbert spaces
by: Boichuk, О. A., et al.
Published: (2023)

Boundary-value problems for the Lyapunov equation. І
by: O. Boichuk, et al.
Published: (2024)

Bounded solutions of the nonlinear Lyapunov equation and homoclinic chaos
by: O. A. Boichuk, et al.
Published: (2019)

On the solvability of a class of discrete matrix equations with cubic nonlinearity
by: Kh. A. Khachatrjan, et al.
Published: (2019)

Boundary-Value problems for systems of integro-differential equations with Degenerate Kernel
by: Boichuk, О. A., et al.
Published: (1996)

On the solvability of a class of discrete matrix equations with a cubic nonlinearity
by: Khachatryan, Kh. A., et al.
Published: (2019)

Analytical construction of the hierarchical matrix Lyapunov function for impulse systems
by: Begmuratov, K. A., et al.
Published: (1997)

Boundary-value problems for the Lyapunov equation. IІ
by: O. Boichuk, et al.
Published: (2024)

Normally solvable operator equations in a Banach space
by: Boichuk, О. A., et al.
Published: (2013)

A criterion for the existence of the unique invariant torus of a linear extension of dynamical systems
by: Boichuk, О. A., et al.
Published: (2007)

Conditions of solvability and submission of solutions of equations with operator matrix in banach spaces
by: Zhuravlev, V. P., et al.
Published: (2023)

Solvability of integrodifferential equations with nondegenerate kernel in Hilbert spaces
by: O. A. Boichuk, et al.
Published: (2023)

Complete Solvability of the Cauchy Problem for Petrovskii Parabolic Equations in S-Type Spaces
by: Litovchenko, V. A., et al.
Published: (2002)

On solvability of the system of matrix equations AX B , BY A over associative rings
by: V. M. Prokip
Published: (2016)

Application of the infinite matrix theory to the solvability of sequence spaces inclusion equations with operators
by: de, Malafosse B., et al.
Published: (2019)

Solvability criterion and representation of solutions of $n$-normal and $d$-normal linear operator equations in a Banach space
by: Zhuravlev, V. F., et al.
Published: (2010)

On the normal solvability of the Tricomi problem for an equation of the Lavrentyev — Bitsadze type
by: Sorokina, N. G., et al.
Published: (1970)

On the solvability of one system of nonlinear Hammerstein-type integral equations on the semiaxis
by: Kh. A. Khachatrjan, et al.
Published: (2017)

Linear Noetherian boundary-value problem for a matrix difference equation
by: Chuiko, S. M., et al.
Published: (2020)

Connected Stability Analysis of Delay Systems via the Matrix-Valued Lyapunov Function
by: Zh. F. San, et al.
Published: (2013)

Connected Stability Analysis of Delay Systems via the Matrix-Valued Lyapunov Function
by: Sun, J.F., et al.
Published: (2013)

On the Unique Solvability of a Nonautonomous Functional Differential Equation of Neutral Type
by: Khusanov, D. Kh., et al.
Published: (2001)

Stochastic Lyapunov Functions for a System of Nonlinear Difference Equations
by: Dzhalladova, I. A., et al.
Published: (2002)

Constructive Estimates of Lyapunov V- Function for Equations of Perturbed Motion
by: A. A. Martynjuk
Published: (2017)

Lyapunov-type inequalities for a nonlinear system including operators
by: M. F. Aktaş, et al.
Published: (2024)

Lyapunov-type inequalities for quasilinear systems with antiperiodic boundary conditions
by: Youyu Wang, et al.
Published: (2013)

Lyapunov-Type Inequalities for Quasilinear Systems with Antiperiodic Boundary Conditions
by: Bai, Yongzhen, et al.
Published: (2013)

Lyapunov-type inequalities for a nonlinear system including operators
by: Aktaş, Mustafa Fahri, et al.
Published: (2024)

On the Solvability of One Class of Nonlinear Integral Equations with a Noncompact Hammerstein–Stieltjes-Type Operator on the Semiaxis
by: Petrosyan, A., et al.
Published: (2015)

Sardaryan T. G. On the solvability of one system of nonlinear Hammerstein-type integral equations on the semiaxis
by: Sardaryan, T. G., et al.
Published: (2017)