Continuing the authors' studies of hybrid dynamical systems, i.e. differential equations governed by finite automata, an efficient and complete classification of control linear systems in the plane is offered. The set of all such systems is divided into equivalence classes which are explicitly characterized by some quantitative invariants. The canonical representatives in each class are determined. It is shown how to use this classification to find out whether a given system is stabilizable or not.

We suggest some criteria for the stabilization of planar linear systems via linear hybrid feedback controls. The results are formulated in terms of the input matrices. For instance, this enables us to work out an algorithm which is directly suitable for a computer realization. At the same time, this algorithm helps to check easily if a given linear 2 × 2 system can be stabilized (a) by a linear ordinary feedback control or (b) by a linear hybrid feedback control.

No abstract

No abstract

The adaptability of grain varieties' productivity is formed in the process of their development under the influence of the environmental conditions of the breeding center, the properties of the initial material and component characteristics due to which the identification of the varieties is carried out. The International Program “Kazakh-Siberian Wheat Improvement for Spring Durum Wheat” (IP KaSibWI SDW) has used the genotypes of seven institutions from Russia and Kazakhstan and their geographic locations as environmental areas. The study of two sets of varieties (25 varieties in 2015-2016 and 26 varieties in 2018) in the KaSib system made it possible to distribute breeding centers according to their “specialization” in the formation of adaptive properties (Malchikov et al., 2018). In particular, there has been found that the staff of the Samara Federal Research Center of the Russian Academy of Sciences, the Samara Research Institute of Agriculture (hereinafter the Samara Research Institute of Agriculture) developed the varieties of wide adaptation (area). Consequently, the traits closely correlating with the productivity on the plots of the Samara ARI may be associated with properties that determine the wide adaptation of varieties. The purpose of the research was to determine the traits correlating with varietal variability of productivity of the KaSib nurseries from Russia and Kazakhstan on the experimental plots of the Samara Research Institute of Agriculture. Field trials were carried out for three years (2015, 2016, 2018); the accounting area of the plots was 10.0 m2, with threefold repetition, with random plot placement; the sheaves for laboratory analysis were taken from each repetition (sampling area of 0.63 m2). Using the methods of correlation and path analysis, there has been established a significant correlation between variation of yield and such traits as economic coefficient (К.хозР), nature weight (H), 1000 grain weight (M1000), sterility of heads in the cenosis (Ст), number of grains per spikelet (ЧЗКК) and number of days before tillering (КДК).