Mathematical methods for the analysis of stability, stabilizability and consensus of linear multiagent systems with discrete time are described. The basis of these methods is the idea of using the notion of joint / generalized spectral radius of matrix sets for analyzing the rate of convergence of matrix products with factors from matrix sets with special properties. The work continues the review of the authors "Consensus in asynchronous multi-agent systems", the first part of which was published in №4.

We review the results of different-scale airborne geophysical survey performed in the territory of the Republic of Rwanda. Such parameters as the modulus of the magnetic field vector, electromagnetic sounding data in time and frequency domain, as well as data from a gamma-ray spectrometer with a total scintillator volume of 32 L were continuously recorded during the flight. The software automatically performed the necessary navigation management on a real-time basis. Automated execution of flight tasks allowed to exclude an operator from the surveying process. It took only 6 months of field works to perform the survey at a scale of 1:50,000 over the area of 26,000 km2, as well as detailing works. The total workscope amounted to 57,718 line km. Maps of anomaly magnetic field and its local part, apparent resistivity maps for the most informative frequency and time channels, Th, U, K concentration maps and Th-K ratio maps have been prepared for a short period of time. Based on the results of map interpretation we selected prospective sites for further study. Detailed airborne survey was performed for 5 sites, and ground geological and geophysical survey was performed for 3 sites. Based on the detailed survey results we selected new local objects associated with quartz-magnetite veined mineralization, dyke bodies, and mafic rock intrusions. Multiple pegmatite intrusions were identified. The information about magnetic, electrical and radiometric characteristics of rocks allowed to reliably classify the identified anomaly objects.

Stabilization of motion of a wheeled robot with constrained control resource by means of a continuous feedback linearizing the closed-loop system in a neighborhood of the target path is considered. The problem of selection of the feedback coefficients is set and discussed. In the case of a straight target path, the desired feedback coefficients are defined to be those that result in the partition of the phase plane into two invariant sets of the nonlinear closed-loop system while ensuring the greatest asymptotic rate of the deviation decrease. A hybrid control law is proposed that ensures the desired properties of the phase portrait and minimal overshooting and is stable to noise. The proposed techniques are extended to the case of circular target paths.

The counter algorithm has been presented to detect pairs of similar numerical strings in order to distinguish between a subset of identical signals and other signals. The pair of similar signals is determined using the matrix of the algorithm. Two elements of the matrix estimate the similarity degree in contrast to the ordinary applied a single value of correlation coefficient. The matching of signal images with the matrix elements has been made on an example of impulse signals. Using this data type we compare the outcomes of two methods: a counter based technique and the correlation method. The difference between the method proposed and the correlation method is discussed.

We propose a family of new measures for edge importance estimation. We focus on weighted directed networks where weights indicate the intensity of connections between nodes. We reward edges that increase node-to-node influence compared to direct connections between them. This approach allows to reveal hidden channels of the influence in networks. We apply the proposed model to food export/import networks in order to elucidate the most important trading relations. We compare the results with edge-betweenness centrality and investigate the interdependence between edge importance and centrality measures of corresponding source and sink nodes. The results are provided in dynamic.