linear

UKRAINIAN ARCHITECTURAL MODERN STYLE IN THE WORKS OF IVAN LEVINSKY

The article considers the formative features of the formation of the Ukrainian architectural style (modern style) as a phenomenon that has accumulated both properties characteristic of the style of Western European countries, and national traditions of the formation of folk housing or sacred construction. Ukrainian architectural style (modern style) has become an outstanding phenomenon in the development of domestic and European architectural art.

Angles between matrices and between polynomials in fractional linear systems and electrical circuits

The notions of angles between matrices and between polynomials of fractional linear systems and electrical circuits are proposed. In analysis of  angles between state matrices of fractional linear systems the Hadamard product of two matrices  is applied. The angles between matrices and their functions are also addressed. The angles between symmetrical and asymmetrical part of matrices are investigated. The angles between polynomials of transfer matrices of fractional linear systems are analyzed and some new properties are established.

Positivity and stability of descriptor linear systems with interval state matrices

The positivity and asymptotic stability of descriptor linear continuous-time and discrete-time systems with interval state matrices and interval polynomials are investigated. Necessary and sufficient conditions for the positivity of descriptor continuous-time and discrete-time linear systems are established. It is shown that the convex linear combination of polynomials of positive linear systems is also the Hurwitz polynomial. The Kharitonov theorem is extended to the positive descriptor linear systems with interval state matrices.

Computation of positive stable realizations for discrete-time linear systems

Sufficient conditions for the existence of positive stable realizations for given proper transfer matrices are established. Two methods are proposed for determination of the positive stable realizations for given proper transfer matrices. The effectives of the proposed procedures is demonstrated on numerical examples.

Positive fractional and cone fractional linear systems with delays

The positive and cone fractional continuous-time and discrete-time linear systems are addressed. Sufficient conditions for the reachability of positive and cone fractional continuous-time linear systems are given. Necessary and sufficient conditions for the positivity and asymptotic stability of the continuous-time linear systems with delays are established. The realization problem for positive fractional continuous-time systems is formulated and solved.