Abstract
It is a well established fact that self-sustained oscillations in autonomous continuous time systems are periodic-the limit cycles in the state plane; for higher order continuous time systems periodic self sustained oscillations are a quite improbable phenomenon which explains the difficulty in obtaining checkable conditions for the existence of such oscillations. At this end V.A. Yakubovich has introduced a new notion of oscillation, called [-/spl alpha/, /spl beta/] output oscillation; for the existence of such solutions checkable existence conditions in the frequency characteristics language are available. The problem of self sustained oscillations for discrete-time systems is quite different from that of the continuous time case; nevertheless the [-/spl alpha/, /spl beta/] oscillation may be introduced for discrete-time systems. The present paper introduces the basic notions in [-/spl alpha/, /spl beta/] oscillations in discrete-time case and gives a frequency-domain criterion of existence for such solutions. The main idea is to obtain exponential instability in the neighborhood of the origin (in the small) and dissipativity (stability in the large).
Published Version
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