Stability of switched systems with average dwell-time
Stability of switched systems with average dwell-time
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DOI：
10.1109/cdc.1999.831330
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发表时间：
1999-12
期刊：
影响因子：
--
通讯作者：
J. Hespanha;A. Morse
中科院分区：
文献类型：
--
作者：
J. Hespanha;A. Morse
结果表明，在稳定线性系统之间的切换，只要切换是“平均慢”的，就会产生稳定系统。特别地，证明了当任意有限区间内的开关数随区间长度线性增长，且增长率足够小时，实现指数稳定性。而且，在所有具有上述性质的开关上，指数稳定性是一致的。对于具有输入的切换系统，这保证了几个输入到状态诱导的规范在所有慢平均切换上是一致有界的。这些结果推广到满足适当均匀性假设的非线性开关系统。本文还表明，在监督控制环境中，尺度无关的迟滞可以产生平均缓慢的切换，因此上述结果可用于研究基于迟滞的自适应控制系统的稳定性。
It is shown that switching among stable linear systems results in a stable system provided that switching is "slow-on-the-average". In particular, it is proved that exponential stability is achieved when the number of switches in any finite interval grows linearly with the length of the interval, and the growth rate is sufficiently small. Moreover, the exponential stability is uniform over all switchings with the above property. For switched systems with inputs this guarantees that several input-to-state induced norms are bounded uniformly over all slow-on-the-average switchings. These results extend to classes of nonlinear switched systems that satisfy suitable uniformity assumptions. In this paper it is also shown that, in a supervisory control context, scale-independent hysteresis can produce switching that is slow-on-the-average and therefore the results mentioned above can be used to study the stability of hysteresis-based adaptive control systems.