论文标题
lurie系统中的收缩和$ k $ - 征收，并应用于网络系统
Contraction and $k$-contraction in Lurie systems with applications to networked systems
论文作者
论文摘要
Lurie系统是线性时间不变系统和非线性反馈功能的互连。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 $，我们的足够条件将根据有限的真实引理和较小的增益条件减少到标准稳定性条件。但是，Lurie系统通常具有超过单个平衡，因此相对于任何规范而言并不依赖。对于$ k = 2 $，我们的状况保证了闭环系统的有序渐近行为：每个有界的解决方案都会收敛到平衡，这不一定是唯一的。我们通过得出通用网络系统的$ K $征收的足够条件来证明我们的结果，然后将其应用于Hopfield神经网络中的$ K $ - 征收，非线性意见动力学模型和2-BUS Power System。
A Lurie system is the interconnection of a linear time-invariant system and a nonlinear feedback function. 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. However, Lurie systems often have more than a single equilibrium and are thus not contractive with respect to any norm. For $k=2$, our condition guarantees a well-ordered asymptotic behaviour of the closed-loop system: every bounded solution converges to an equilibrium, which is not necessarily unique. We demonstrate our results by deriving a sufficient condition for $k$-contraction of a general networked system, and then applying it to guarantee $k$-contraction in a Hopfield neural network, a nonlinear opinion dynamics model, and a 2-bus power system.
