Abstract
Abstract In this paper some connections of mathematical system theory with the problem of absolute stability of control systems are pointed out. The absolute stability problem was formulated in the early 1940s starting from some practical control problems. The considerable development of this problem in the last 25 years has been profitable for mathematical system theory. At the same time concepts of system theory provided an adequate context for a deep understanding of this problem. Such system theory concepts as blocks, interconnections, isomorphism between time domain representations, and complex domain characteristics showed themselves very useful in absolute stability and hyperstability studies. Among the main contributions of absolute stability and hyperstability studies to mathematical system theory development one can cite the concept of “block plus integral index” and the system theory interpretation of Bochner's theorem on positive functions.
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