描述线性离散系统控制能力的解析因子
Analytical Factors for Describing the Control Ability of Linear Discrete-time Systems
摘要：
本文首先讨论了由具有$n$不同或重复实特征值的矩阵对生成的环带拓扑的解析体积计算，然后通过解构体积计算方程，构造了3类形状因子。这些分析的体积和形状因子可以准确地描述小生境的大小和形状。由于单位输入变量（即输入变量有界值为1）的LDT系统的控制能力与能控域\cite{zhaomw202003}直接相关，基于这些体积和形状因子的解析表达式，可以方便地量化控制能力。通过选取这些解析表达式作为目标函数或约束条件，可以建立一种新的控制能力优化问题和求解方法。通过优化，不仅提高了系统的开环控制能力，而且提高了系统的一些闭环控制性能，如控制策略的最优时间消耗、鲁棒性等，与\cite{zhaomw202003}的结论一致。
英文摘要：
In this paper, the analytical volume computations of the zonotopes generated by the matrix pair with $n$ different or repeated real eigenvalues are discussed firstly, and then by deconstructing the volume computing equations, 3 classes of the shape factors are constructed. These analytical volume and shape factors can describe accurately the size and shape of the zonotopes. Because the control ability for LDT systems with the unit input variables (i.e. the input variable is with bounded value as 1) is directly related to the controllability region \cite{zhaomw202003}, based on these analytical expressions on the volume and shape factors, the control ability can be quantized conveniently. By choosing these analytical expressions as the objective function or constraint conditions, a novel optimizing problems and solving method for the control ability can be founded. Based on the optimization, not only the open-loop control ability, and but also the some closed-loop control performance, such as the optimal time waste, robustness of the control strategy, etc, can be promoted, according to the conclusions in paper \cite{zhaomw202003}.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
