Dwell time for switched systems with multiple equilibria on a finite time-interval
Dwell time for switched systems with multiple equilibria on a finite time-interval
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发表时间：
2017-03
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通讯作者：
O. Makarenkov;A. Phung
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作者：
O. Makarenkov;A. Phung
我们描述了具有多个全局指数稳定均衡的切换系统的解的行为。我们引入了理想吸引子，并表明，如果切换频率慢于合适的驻留时间 $T$，则切换系统的解将保持在理想吸引子的任何给定 $\varepsilon$ 膨胀中。此外，我们还给出了确保 $\varepsilon$ 通货膨胀是全球吸引子的条件。最后，我们研究了切换次数的增加对解决方案从一个区域到达另一区域所需的总时间的影响。
We describe the behavior of solutions of switched systems with multiple globally exponentially stable equilibria. We introduce an ideal attractor and show that the solutions of the switched system stay in any given $\varepsilon$-inflation of the ideal attractor if the frequency of switchings is slower than a suitable dwell time $T$. In addition, we give conditions to ensure that the $\varepsilon$-inflation is a global attractor. Finally, we investigate the effect of the increase of the number of switchings on the total time that the solutions need to go from one region to another.