This paper concerns systems with two features, both related to "real world" practical systems and to the fact that trying to idealize the mathematical model of the system is often not justified and leads to erroneous conclusions. Firstly, the paper is concerned with non-linear elements in the system, as are most "real world" engineering systems. Secondly, the paper allows interval uncertainty in the coefficients of the linear part of the system. The price, which has to be paid for taking into account these realistic conditions, is in the complexity of the analysis and the difficulties in analytlc solutions. These difficulties, however, can be overcome to an extent, by using approximate methods. The present paper belongs to this class of approaches.One of the possible descriptions of a large class of non-linear systems is where an input nonlinear element is cascaded by a linear time-invariant plant, and the output is fed back to the input to form a closed loop system. If our knowledge of the non-linear element is limited, it is natural to assume that it belongs to a sector (a Lure type system). Such systems have been long studied in the literature since 1961 111 (for the time invariant case) and 1963 [2] (for the time-varying case). Recently (except for an early study in 1969 [3]), such systems have also been studied for the case where uncertainties in the coefficients of the linear part are assumed [41-11 11.In this paper new approaches to the stability analysis and limit cycle occurrence. of such systems are proposed. These approaches enable the designer to explicitly detect the presence of possible limit cycles including the range of their frequencies and the range of their amplitudes, a feature, which has not been achieved in the past. The price for this is that we assume some knowledge about the type of the non-linear element, e.g. a saturation actuator, which is very frequently used in such systems.The present paper, like [14], assumes a known characteristic of the non-linear part (single valued), uses the SIDF (sinusoidal input describing function) approach, and assumes interval uncertainties in the coefficients of the linear plant's transfer function. However, it extends the results of 1141 in the following ways: I. We describe a different and explicit method to determine the set of possible intersections of the family of Nyquist plots with the SIDF in the real case, thus detecting the possible limit cycles. This becomes possible in a very simple way, by noticing that this set must be the intersection of two sets, which can be determined by a simple sign rule.2. We can explicitly determine the range of frequencies of the possible limit cycles, as well as the range of amplitudes of these limit cycles. The computations are relatively simple.A numerical example is provided. Simulations carried out on this example withour applying the SIDF approximation indicate that the error in the above ranges of frequencies and amplitudes is not significant. 234

Генезис и психологическое содержание научной проблемы лояльности В результате историко-психологического анализа общественнофилософской рефлексии феномена лояльности выделены ее основные этапы, обозначены авторы и ключевые идеи, внесшие наибольший вклад в формирование современного понимания психологической сущности лояльности. Усложнение социальных реалий, ведущее к актуализации вопросов социальной самоидентификации и ее реализации в поведении, рассматривается как основная предпосылка развития представлений о лояльности и постановки научной проблемы лояльности. Сделаны выводы о психологическом содержании научной проблемы лояльности. Ключевые слова: лояльность; социальная идентификация; нормативный порядок; реализация идентичности.

The article discusses the administrative-legal and phenomenological approaches to understanding the official loyalty. Official loyalty is being considered under the administrative-legal approach as adherence to formal official duty, which is a system of obligations, taken together with official status, the source of which are: normative base of service activity, legal requirements of the head and public interests. Lists of the limitations of administrative-legal approach to understanding the of official loyalty: weak underdeveloped concept, the failure to take into account the wide range of situations, operation with a models rather than actual processes. Discusses the advantages of the phenomenological approach in studying the performance of loyalty: its psychological advantages, the existence of a theoretical framework, the work with the real phenomena. Within the phenomenological approach official loyalty is defined as psychological-behavioral integration of the employee in the group operating in the service sector, on the basis of a common cause of activities. Possibilities of sharing of the considered approaches for the decision of problems of optimization of official activity are designated.

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The article suggests a solution to the previously raised problem of contradictions of administrative-legal and phenomenological approaches to assessing loyalty of law enforcing governmental employees. It is shown that the application of the phenomenological approach in combination with the administrative-legal approach is not just expedient, but necessary. Argued that loyalty to the formal social group «governmental employees» can not be estimated directly from the point of view of socio-psychological criteria, since it is not a group subject with a formed psycho-behavioral pattern shared by group members. It is suggested that the term «loyalty» is conditionally applicable for assessing loyalty to the group «governmental employees» and similar formal groups. The authors propose an indirect way of assessing loyalty to formal groups of governmental employees, created and tested by S.V. Gornostaev in researching the official loyalties of the staff of the Russian penitentiary system. This method involves the identification of groups operating in the professional and service environment, which the employee has formed loyalty and comparison of key norms of these groups with formal norms.