New equivalent conditions of the asymptotical stability and stabilization of positive linear dynamical systems are investigated in this paper. The asymptotical stability of the positive linear systems means that there is a solution for linear inequalities systems. New necessary and sufficient conditions for the existence of solutions of the linear inequalities systems as well as the asymptotical stability of the linear dynamical systems are obtained. New conditions for the stabilization of the resultant closed-loop systems to be asymptotically stable and positive are also presented. Both the stability and the stabilization conditions can be easily checked by the so-called I-rank of a matrix and by solving linear programming (LP). The proposed LP has compact form and is ready to be implemented, which can be considered as an improvement of existing LP methods. Numerical examples are provided in the end to show the effectiveness of the proposed method.

The article presents an analysis of the change in air voids in asphalt mixtures subjected to fatigue tests at three temperatures of 0°C, 10°C and 25°C. The X-ray computerized tomography imaging method, XCT, was used to identify the air voids in the samples. The research allowed to determine changes in the content of air voids in subsequent fatigue cycles in the sample area. The relationship between air voids volume and the stiffness modulus value was also determined during fatigue for three temperatures. The largest changes were found in samples with notches at 0°C. The analysis of the change in the content of air voids showed that the micro-cracking nucleation processes develop with the number of fatigue cycles. Using the numerical model finite element method we determined the distribution and change in fatigue damage in the extreme areas of the sample during various stages of fatigue. We found clear relationship between the damage and the increased content of air voids.