A measure of quality of a control system is a quantitative extension of the classical binary notion of controllability. In this article we study the quality of linear control systems from a frame-theoretic perspective. We demonstrate that all LTI systems naturally generate a frame on their state space, and that three standard measures of quality involving the trace, minimum eigenvalue, and the determinant of the controllability Gramian achieve their optimum values when this generated frame is tight. Motivated by this, and in view of some recent developments in frame-theoretic signal processing, we propose a natural measure of quality for continuous time LTI systems based on a measure of tightness of the frame generated by it and then discuss some properties of this frame-theoretic measure of quality.

控制系统质量的度量是对可控性经典二进制概念的定量扩展。在本文中，我们从框架理论的角度研究线性控制系统的质量。我们证明了所有LTI系统自然会在其状态空间上生成一个框架，并且当此生成的框架很紧时，涉及迹线，最小特征值和可控制性革兰氏决定因素的三种质量标准度量可以达到其最佳值。因此，鉴于帧理论信号处理的一些最新发展，我们提出了一种基于连续时间LTI系统产生的帧的紧密度的自然度量方法，然后讨论了该帧的一些特性。 -质量的理论量度。