In this paper, we relate the feedback canonical form FBCF [24] of differential-algebraic control systems (DACSs) with the famous Morse canonical form MCF [28],[27] of ordinary differential equation control systems (ODECSs). First, a procedure called an explicitation (with driving variables) is proposed to connect the two above categories of control systems by attaching to a DACS a class of ODECSs with two kinds of inputs (the original control input $u$ and a vector of driving variables $v$). Then, we show that any ODECS with two kinds of inputs can be transformed into its extended MCF via two intermediate forms: the extended Morse triangular form and the extended Morse normal form. Next, we illustrate that the FBCF of a DACS and the extended MCF of the explicitation system have a perfect one-to-one correspondence. At last, an algorithm is proposed to transform a given DACS into its FBCF via the explicitation procedure and a numerical example is given to show the efficiency of the proposed algorithm.

在本文中，我们将微分代数控制系统 (DACS)的反馈规范形式FBCF [24] 与常微分方程控制系统 (ODECS)的著名莫尔斯规范形式MCF [28]、[27] 联系起来。首先，提出了一种称为显化（带有驱动变量）的程序，通过将一类具有两种输入（原始控制输入$你$ 和驱动变量的向量 $v$）。然后，我们证明了任何具有两种输入的 ODECS 都可以通过两种中间形式转换为其扩展的MCF：扩展的莫尔斯三角形式和扩展的莫尔斯范式。接下来，我们说明了FBCF一个DACS和扩展MCF的明晰化系统拥有完美的一对一一对应。最后，提出了一种通过显式过程将给定的DACS转换为其FBCF的算法，并给出了一个数值例子来说明所提出算法的效率。