论文标题
$ k $ - 征收lurie Systems的足够条件
A sufficient condition for $k$-contraction in Lurie systems
论文作者
论文摘要
我们考虑通过线性时间不变系统和非线性反馈功能获得的Lurie系统。这样的系统通常具有超过单个平衡，因此相对于任何规范而言并不依赖。我们为Lurie系统的$ k $征收提供了一种新的足够条件。对于$ k = 1 $，我们的足够条件将根据有限的真实引理和较小的增益条件减少到标准稳定性条件。对于$ k = 2 $，我们的状况保证了闭环系统的排序渐近行为：每个有界解决方案都会收敛到平衡，这不一定是唯一的。我们将结果应用于网络系统的$ K $缩短率的足够条件。
We consider a Lurie system obtained via a connection of a linear time-invariant system and a nonlinear feedback function. Such systems often have more than a single equilibrium and are thus not contractive with respect to any norm. We derive a new sufficient condition for $k$-contraction of a Lurie system. For $k=1$, our sufficient condition reduces to the standard stability condition based on the bounded real lemma and a small gain condition. For $k=2$, our condition guarantees well-ordered asymptotic behaviour of the closed-loop system: every bounded solution converges to an equilibrium, which is not necessarily unique. We apply our results to derive a sufficient condition for $k$-contractivity of a networked system.
