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.
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.
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.
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.