Time-Delay Systems: Lyapunov Functionals and Matrices

Stability is one of the most studied issues in the theory of time-delay systems, but the corresponding chapters of published volumes on time-delay systems do not include a comprehensive study of a counterpart of classical Lyapunov theory for linear delay free systems. The principal goal of the book is to fill this gap, and to provide readers with a systematic and exhaustive treatment of the basic concepts of the Lyapunov-Krasovskii approach to the stability analysis of linear time-delay systems. The book is organized into two parts. The first part is dedicated to the case of retarded type time-delay systems; it consists of four chapters, which respectively deal with results concerning the existence and uniqueness of the solutions of an initial value problem, the class of linear systems with one delay, the case of systems with several delays, and the case of systems with distributed delays. The second part of the book studies the case of neutral type time-delay systems, containing three chapters that extend the results presented earlier in the book to neutral time-delay systems and treating special classes of linear time-delay systems.  Time-Delay Systems: Lyapunov Functionals and Matrices will be of great use and interest to researchers and graduate students in automatic control and applied mathematics as well as practicing engineers involved in control system design

ACCEPTED TO IEEE TRANSACTIONS ON AUTOMATIC CONTROL UNDER REVISION (JUNE 2003) 1 Static

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Analysis of Theory and Practice of Evaluation of the Influence of the Results of the Modernization of Weapons and Military Equipment on the Combat Possibilities of the Armed Forces of the Armed Forces of Ukraine

Significant changes in the military-political, socio-economic and demographic state of Ukraine that have occurred in recent years have caused the need to develop new approaches to ensuring its national security, including the definition and clarification of: the tasks of the Armed Forces, their role and place in the structure the security and defense sectors of Ukraine; scientifically substantiated goals of reforming the Armed Forces; the composition and structure of the services of the Armed Forces, combat arms and special forces, which can optimally ensure armed protection of national interests, territorial integrity of Ukraine; a cost estimate of the costs required to implement plans to reform the Armed Forces and to maintain them at the required level of combat and mobilization readiness; the economic capabilities of the state to meet the needs of the Armed Forces, which are due to the need to solve the tasks assigned to them, and the like. One of the main issues of the further development of the Armed Forces of Ukraine today is the quality and completeness of the solution to the issues of military-technical policy. The degree of implementation of which directly affects the state and technical equipment of the Armed Forces and depends on many components that create both positive and negative effects on the state and further development of the Armed Forces. The main role in this process is played by the financing of the needs of the Armed Forces of Ukraine in the required volume, as well as the scientific substantiation of medium-term and long-term plans for the development of weapons and military equipment. When developing them, it is necessary to be based on the needs of ensuring the required level of defense capability by finding the optimal balance between the defensive needs and economic capabilities of the state, on the one hand, and the combat and technical characteristics of weapons and military equipment, on the other hand. It is on the state of financing of defense needs that the degree of fulfillment of the tasks of equipping the Armed Forces of Ukraine with the latest or modernized models of weapons and military equipment depends. This raises the problem of finding the most optimal (expedient), from a military and economic point of view, ways to provide the Armed Forces of Ukraine with samples of weapons and military equipment. The authors in the article present the results of the analysis of the theory and practice of assessing the impact of the results of modernization of weapons and military equipment on the combat capabilities of military formations, as well as the factors that affect them. The analysis was carried out in the following areas: analysis and assessment of the impact of modernization on the level of combat capabilities of a military formation; analysis of the modernization of the Armed Forces of Ukraine; analysis of the existing methodological apparatus for determining the requirements for quantitative and qualitative characteristics in the modernization of weapons and military equipment. Based on the results obtained, the authors have proposed a number of recommendations for further research on improving the combat capabilities of the Armed Forces of Ukraine, taking into account the results of modernization of weapons and military equipment in the formation of medium-term and long-term development programs

4-(Aryl)-Benzo[4,5]imidazo[1,2-<i>a</i>]pyrimidine-3-Carbonitrile-Based Fluorophores: Povarov Reaction-Based Synthesis, Photophysical Studies, and DFT Calculations

A series of novel 4-(aryl)-benzo[4,5]imidazo[1,2-a]pyrimidine-3-carbonitriles were obtained through the Povarov (aza-Diels–Alder) and oxidation reactions, starting from benzimidazole-2-arylimines. Based on the literature data and X-ray diffraction analysis, it was discovered that during the Povarov reaction, [1,3] sigmatropic rearrangement leading to dihydrobenzimidazo[1,2-a]pyrimidines took place. The structures of all the obtained compounds were confirmed based on the data from 1H- and 13C-NMR spectroscopy, IR spectroscopy, and elemental analysis. For all the obtained compounds, their photophysical properties were studied. In all the cases, a positive emission solvatochromism with Stokes shifts from 120 to 180 nm was recorded. Aggregation-Induced Emission (AIE) has been illustrated for compound 6c using different water fractions (fw) in THF. The compounds 6c and 6f demonstrated changes in emission maxima or/and intensities after mechanical stimulation