Partial stability and control
Partial stability and control
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DOI：
10.1007/978-1-4612-4150-8
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
V. I. Vorotnikov
中科院分区：
文献类型：
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作者：
V. I. Vorotnikov
与一般稳定性理论的传统研究不同，这一monograph处理的问题是关于动态系统的稳定性和镇定，而不是关于所有的，而是仅仅关于表征这些系统的变量的给定部分。这类问题通常被称为局部稳定性问题（稳定化问题）。它们自然出现在应用中，无论是从系统的适当性能的要求，或在评估系统的能力。此外，许多实际的（或期望的）现象可以根据这些问题来表述，并以这些问题为基础进行分析。可以指出以下多方面的现象和问题：·”Lotka-Volterra灭绝生态学原理";·电磁场中粒子的聚焦和加速;·陀螺仪轴的”漂移”;·通过与航天器相连的转子的特殊安排的相对运动来稳定航天器。解决稳定性问题的方法也非常有效。基于部分稳定性（稳定化）的初步分析，相对于所有变量的稳定化。AM李雅普诺夫，现代稳定性理论的创始人，是第一个制定部分稳定性问题。后来，VV Rumyan tsev的作品引起了世界各地许多数学家和机械师对这个问题的注意，这导致了它的深入研究。李雅普诺夫函数方法成为研究这一问题的关键方法，它在分析理论和应用问题上都是非常有效的。
Unlike the conventional research for the general theory of stability, this mono graph deals with problems on stability and stabilization of dynamic systems with respect not to all but just to a given part of the variables characterizing these systems. Such problems are often referred to as the problems of partial stability (stabilization). They naturally arise in applications either from the requirement of proper performance of a system or in assessing system capa bility. In addition, a lot of actual (or desired) phenomena can be formulated in terms of these problems and be analyzed with these problems taken as the basis. The following multiaspect phenomena and problems can be indicated:•" Lotka-Volterra ecological principle of extinction;"• focusing and acceleration of particles in electromagnetic fields;•" drift" of the gyroscope axis;• stabilization of a spacecraft by specially arranged relative motion of rotors connected to it. Also very effective is the approach to the problem of stability (stabilization) with respect to all the variables based on preliminary analysis of partial sta bility (stabilization). AM Lyapunov, the founder of the modern theory of stability, was the first to formulate the problem of partial stability. Later, works by VV Rumyan tsev drew the attention of many mathematicians and mechanicians around the world to this problem, which resulted in its being intensively worked out. The method of Lyapunov functions became the key investigative method which turned out to be very effective in analyzing both theoretic and applied problems.