Self-sustained oscillations in discrete-time nonlinear feedback systems
Self-sustained oscillations in discrete-time nonlinear feedback systems
复制标题
离散时间非线性反馈系统中的自持振荡
DOI：
10.1109/melcon.1998.692490
复制
发表时间：
1998
期刊：
影响因子：
--
通讯作者：
V. Rǎsvan
中科院分区：
文献类型：
--
作者：
V. Rǎsvan
一个公认的事实是，自主连续时间系统的自持续振荡是周期性的——状态面上的极限环；对于高阶连续时间系统，周期自持续振荡是一种非常不可能的现象，这解释了为什么很难得到这种振荡存在的可检验条件。为此，va Yakubovich引入了一种新的振荡概念，称为[-/spl alpha/， /spl beta/]输出振荡；对于这些解的存在性，在频率特性语言中提供了可检查的存在条件。离散系统的自持续振动问题与连续系统的自持续振动问题有很大的不同；然而，离散时间系统可能引入[-/spl α /， /spl β /]振荡。本文介绍了离散情况下[-/spl α /， /spl β /]振动的基本概念，并给出了这类振动解的频域存在性判据。主要思想是获得原点附近的指数不稳定性（“在小范围内”）和耗散率（“在大范围内稳定”）。
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").