论文标题
关于$ K $阳性线性系统的对角线稳定性
On the Diagonal Stability of $k$-Positive Linear Systems
论文作者
论文摘要
我们考虑$ k $阳性的线性系统，即绘制自身最多$ k-1 $符号变体的向量集的系统。对于$ k = 1 $，这将减少到正线性系统。众所周知，稳定的正线性时间不变（LTI）系统允许对角Lyapunov功能。该属性具有许多重要的含义。一个自然的问题是稳定的$ k $ - 阳性系统是否承认对角Lyapunov功能。本文表明，总的来说，答案是否定的。但是，对于$（n-1）$的连续时间和离散时间$ n $二维系统，我们为对角稳定性提供了足够的条件。
We consider $k$-positive linear systems, that is, systems that map the set of vectors with up to $k-1$ sign variations to itself. For $k=1$, this reduces to positive linear systems. It is well-known that stable positive linear time invariant (LTI) systems admit a diagonal Lyapunov function. This property has many important implications. A natural question is whether stable $k$-positive systemsalso admit a diagonal Lyapunov function. This paper shows that, in general, the answer is no. However, for both continuous-time and discrete-time $n$-dimensional systems that are $(n-1)$-positive we provide a sufficient condition for diagonal stability.
