2018
Том 70
№ 9

All Issues

Mazko A. G.

Articles: 13
Article (Ukrainian)

Stability Criteria and Localization of the Matrix Spectrum in Terms of Trace Functions

Mazko A. G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2014. - 66, № 10. - pp. 1379–1386

New necessary and sufficient conditions for the asymptotic stability and localization of the spectra of linear autonomous systems are proposed by using the matrix trace functions. The application of these conditions is reduced to the solution of two scalar inequalities for a symmetric positive-definite matrix. As a corollary, for linear control systems, we present a procedure aimed at the construction of the set of stabilizing measurable output feedbacks.

Article (Russian)

Localization of eigenvalues of polynomial matrices

Mazko A. G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2010. - 62, № 8. - pp. 1063–1077

We consider the problem of localization of eigenvalues of polynomial matrices. We propose sufficient conditions for the spectrum of a regular matrix polynomial to belong to a broad class of domains bounded by algebraic curves. These conditions generalize the known method for the localization of the spectrum of polynomial matrices based on the solution of linear matrix inequalities. We also develop a method for the localization of eigenvalues of a parametric family of matrix polynomials in the form of a system of linear matrix inequalities.

Article (Ukrainian)

Cone inequalities and stability of differential systems

Mazko A. G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2008. - 60, № 8. - pp. 1058–1074

We investigate generalizations of classes of monotone dynamical systems in a partially ordered Banach space. We establish algebraic conditions for the stability of equilibrium states of differential systems on the basis of linearization and application of derivatives of nonlinear operators with respect to a cone. Conditions for the positivity and absolute stability of a certain class of differential systems with delay are proposed. Several illustrative examples are given.

Article (Ukrainian)

Invariant cones and stability of linear dynamical systems

Aliluiko A. M., Mazko A. G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 11. - pp. 1446–1461

We present a method for the investigation of the stability and positivity of systems of linear differential equations of arbitrary order. Conditions for the invariance of classes of cones of circular and ellipsoidal types are established. We propose algebraic conditions for the exponential stability of linear positive systems based on the notion of maximal eigenpairs of a matrix polynomial.

Article (Russian)

Stability and Comparison of States of Dynamical Systems with Respect to a Time-Varying Cone

Mazko A. G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2005. - 57, № 2. - pp. 198–213

We investigate classes of dynamical systems in a partially ordered space with properties of monotonicity type with respect to specified cones. We propose new methods for the stability analysis and comparison of solutions of differential systems using time-varying cones. To illustrate the results obtained, we present examples using typical cones in vector and matrix spaces.

Article (Russian)

Stability of positive and monotone systems in a partially ordered space

Mazko A. G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2004. - 56, № 4. - pp. 462–475

We investigate properties of positive and monotone dynamical systems with respect to given cones in the phase space. Stability conditions for linear and nonlinear differential systems in a partially ordered space are formulated. Conditions for the positivity of dynamical systems with respect to the Minkowski cone are established. By using the comparison method, we solve the problem of the robust stability of a family of systems.

Article (Russian)

Positive and Monotone Systems in a Partially Ordered Space

Mazko A. G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2003. - 55, № 2. - pp. 164-173

We investigate properties of positive and monotone differential systems with respect to a given cone in the phase space. We formulate criteria for the stability of linear positive systems in terms of monotonically invertible operators and develop methods for the comparison of systems in a partially ordered space.

Article (Russian)

Stability of Linear Positive Systems

Mazko A. G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2001. - 53, № 3. - pp. 323-330

We establish criteria of asymptotic stability for positive differential systems in the form of conditions of monotone invertibility of linear operators. The structure of monotone and monotonically invertible operators in the space of matrices is investigated.

Article (Russian)

Localization of the spectrum and representation of solutions of linear dynamical systems

Mazko A. G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 10. - pp. 1341–1351

We develop a general method for the localization of eigenvalues of matrix polynomials and functions based on the solution of matrix equations. For a broad class of equations, we formulate theorems that generalize the known properties of the Lyapunov equation. A new method for the representation of solutions of linear differential and difference systems is proposed.

Article (Russian)

Distribution of the spectrum and representation of solutions of degenerate dynamical systems

Mazko A. G.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 7. - pp. 930–936

We propose algebraic methods for the investigation of the spectrum and structure of solutions of degenerate dynamical systems. These methods are based on the construction and solution of new classes of matrix equations. We prove theorems on the inertia of solutions of the matrix equations, which generalize the well-known properties of the Lyapunov equation.

Article (Ukrainian)

Semiinversion and properties of matrix invariants

Mazko A. G.

Full text (.pdf)

Ukr. Mat. Zh. - 1988. - 40, № 4. - pp. 525-528

Article (Ukrainian)

Distribution of the spectrum of a regular matrix pencil with respect to plane curves

Mazko A. G.

Full text (.pdf)

Ukr. Mat. Zh. - 1986. - 38, № 1. - pp. 116–120

Article (Ukrainian)

An estimate of the location of the spectrum of a matrix relative to plane curves

Mazko A. G.

Full text (.pdf)

Ukr. Mat. Zh. - 1985. - 37, № 1. - pp. 38 – 42