Abstract
Simple criteria for the observability of elastic systems are established. Theorems are proved that enable one to determine whether distributed controllable systems, whether linear or non-linear, are asymptotically stable, by examining a model not involving elasticity. The results are obtained without truncation of elastic modes. Elasticity in the structure of controlled objects may modify the characteristics of the system to such a degree that a control system developed without allowing for elasticity, or allowing for only a few modes of elastic vibration, does not guarantee stability of the real physical system, since it may lead to instability in the omitted modes. A further complication is the approximate nature of dynamical schemes for real controlled objects; the only more or less reliable parameters are those relating to the lowest elastic modes. In addition, the output characteristics of the various sensors and actuating elements are usually non-linear and governed by differential equations. Hence the importance of developing methods for the synthesis and analysis of non-linear control systems for objects with inaccurately specified characteristics, in such a way as to guarantee asymptotic stability of the state of equilibrium of the full system without truncation of elastic vibratory modes. This problem will be solved in the present paper.
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