Анализ устойчивости некоторых крупномасштабных систем

Аннотация

Subjects of research: The job has theoretical Character. Here is considered (examined) mathematical models linear and nonlinear large-scale system, izodrom of a regulator and longitudinal movement plane. Purpose of work: development of criteria of stability (asyptotic stability) and instability a condition of balance of linear and nonlinear large-scale systems. The application of the received results to tasks of stability izodrom of a regulator and longitudinal movement of the plane Method of research: Direct method Lyapunovs, method a matrix Function Lyapunovs and some methods of the theoretical mechanics, theory of stability of movement. The results achieved and their novelty: the scientific novelty of the received results of the dissertation consists in the following: the new concept generalized transpontions of matrixes is entered and is investigated of their properties; the analysis of structure linear large - scale systems is given: the sufficient conditions of stability a condition of balance linear large - scale systems are received; the sufficient conditions a condition of balance nonlinear large - scale systems arc established; is received sufficient conditions of stability of nonlinear adjustable systems; the new sufficient conditions of stability izodrom of a regulator and longitudinal movement of the plane arc found. Practical value: practical applicability received results is proved by research asymptotic stability izodrom of a regulator and longitudinal movement of the plane, and also by analysis of a numbcr(line) of modelling examples. Degree of embed and economic effectivity: techniques and the received results can be introduced for the decisions of a task stability of a wide class of mechanical systems. The job carries theoretical character the received results of the dissertation allow more deeply to investigate stability of mechanical systems simulated by large-scale systems. Sphere of usage: the basic results of the dissertation have theoretical character. Them it is possible will apply to research of stability of various mechanical systems. It is proved by research asymptotic stability izodrom of a regulator and longitudinal movement of the plane, and also by analysis of a number (line) of modelling examples.