论文标题
正线性离散时间系统的稳定性标准
Stability criteria for positive linear discrete-time systems
论文作者
论文摘要
我们证明了在小增益条件下，在有序的BANACH空间中，正线性离散时间系统的指数稳定性的新特征。这种条件在有限维系统理论中起着重要作用，但在无限维度的环境中相对尚未探索。 我们的结果适用于具有正常且产生正锥的有序BANACH空间的离散时间系统。此外，我们表明，如果圆锥体具有非空内部或所考虑的运算符，我们的稳定性标准可以大大简化。 为了将结果置于上下文中，我们概述了已知的稳定性标准（不一定是正面）操作员，并为来自该领域的几种民间传说特征提供了完整的证明。
We prove new characterisations of exponential stability for positive linear discrete-time systems in ordered Banach spaces, in terms of small-gain conditions. Such conditions have played an important role in the finite-dimensional systems theory, but are relatively unexplored in the infinite-dimensional setting, yet. Our results are applicable to discrete-time systems in ordered Banach spaces that have a normal and generating positive cone. Moreover, we show that our stability criteria can be considerably simplified if the cone has non-empty interior or if the operator under consideration is quasi-compact. To place our results into context we include an overview of known stability criteria for linear (and not necessarily positive) operators and provide full proofs for several folklore characterizations from this domain.
