论文标题
在空间互连系统的稳定性方面的阳性三角多项式
Positive Trigonometric Polynomials on the Stability of Spatially Interconnected Systems
论文作者
论文摘要
本文致力于通过正相（SOS）阳性三角多项式分解的空间互连系统（SISS）的稳定性分析。对于SISS的每个空间方向，考虑了三种类型的互连结构。受到有理参数化和可靠的稳定性函数的想法的启发，得出了必要和足够的条件，以分别建立具有两个不同组合拓扑的SISS的稳定性。对于这些结果，主要问题涉及三角多项式的全球或局部积极性。使用SOS分解和阳性三角多项式的广义痕量参数化，因此可以通过两个半决赛（SDP）来量化解决问题的问题。由于假设空间可逆性，提出的方法适用于所有可能的互连结构。给出数值示例以说明派生理论结果的效率。
This paper is devoted to the stability analysis of spatially interconnected systems (SISs) via the sum-of-squares (SOS) decomposition of positive trigonometric polynomials. For each spatial direction of SISs, three types of interconnected structures are considered. Inspired by the idea of rational parameterization and robust stabilizability function, necessary and sufficient conditions are derived for establishing the stability of SISs with two different combined topologies respectively. For these results, the primary issue concerns the global or local positivity of trigonometric polynomials. SOS decomposition and generalized trace parameterization of positive trigonometric polynomials are utilized so that the addressed problems can be quantified by two semidefinite programs (SDPs). The proposed methods are applicable to all possible interconnected structures due to the assumption of spatial reversibility. Numerical examples are given to illustrate the efficiency of the derived theoretical results.
