Abstract
Constrained switching of switched nonlinear systems consists of many classes of switching signals with markedly different features. One of the most important ones is the average dwell time (ADT) switching. For switched systems, it is a well-known result that a switched nonlinear system is globally uniformly asymptotically stable under arbitrary switching sequence if the ADT satisfies the lower bound defined by a real constant value ( ). In this note, it will be shown that this ADT condition is also necessary.
Highlights
The theory of switched systems has matured into an important field of research
The former refers to those systems where switch is triggered by system states satisfying certain prescribed conditions, while the latter implies that the system is switched according to a time sequence
For aircraft engines working over a large flight envelope, their control systems need to be switched among a variety of controllers
Summary
The theory of switched systems has matured into an important field of research. Its development has been motivated by the fact that many dynamical systems can be represented by a series of subsystems or modes, scheduled by switches among these modes. The former refers to those systems where switch is triggered by system states satisfying certain prescribed conditions (guard conditions), while the latter implies that the system is switched according to a time sequence For both classes of switched systems, abounding examples exist in biological and engineering systems. To guarantee stability under arbitrary switching, the common Lyapunov function method plays an important role. This is because the existence of a Jiqiang Wang: The Average Dwell Time Condition τa. It is generally recognized that the common Lyapunov function approach to guarantee GUAS under arbitrary switching is very conservative and in many applications the average dwell time (ADT) switching is meaningful and flexible. ADT switching precludes randomly fast switching signals and avoids Zeno behaviour
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