作者:
JP Hespanha，/S Morse
关键词:
adaptive control ； asymptotic stability ； hysteresis ； linear systems ； nonlinear systems ； average dwell-time ； exponential stability ； hysteresis-based adaptive control ； input-to-state induced norms ； nonlinear switched systems
摘要:
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
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