论文标题
线性离散时间系统的有限时间可控区域的分析量分析
Analytical Volume Analysis for the Finite-time Controllable Region of the Linear Discrete-time Systems
论文作者
论文摘要
In this paper, the works on the analytical volume analysis for the controllable regions of the linear discrete-time (LDT) systems in papers \cite{zhaomw202001} and \cite {zhaomw202004} are discussed further and a new theorem on the analytical computing for the finite-time controllability zonotope (controllable region) of LDT systems are proven.然后，描述系统控制能力的三个分析因素是从可控区域的分析体积表达中成功解构的。最后，定理被概括为三种情况：狭窄的可控区域，矩阵$ a $，带有$ n $ n $负征值，线性连续时间系统。
In this paper, the works on the analytical volume analysis for the controllable regions of the linear discrete-time (LDT) systems in papers \cite{zhaomw202001} and \cite {zhaomw202004} are discussed further and a new theorem on the analytical computing for the finite-time controllability zonotope (controllable region) of LDT systems are proven. And then, three analytical factors describing the control capability of the systems are deconstructed successfully from the analytical volume expression of the controllable region. Finally, the theorem is generalized to three cases: the narrow controllable region, the matrix $A$ with $n$ negative eigenvalues, the linear continuous-time systems.
