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arXiv · 2103.14913

From Morse Triangular Form of ODE Control Systems to Feedback Canonical Form of DAE Control Systems

Yahao Chen·Witold Respondek
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Abstract

In this paper, we relate the feedback canonical form \textbf{FNCF} of differential-algebraic control systems (DACSs) with the famous Morse canonical form \textbf{MCF} 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 \textbf{MCF} via two intermediate forms: the extended Morse triangular form and the extended Morse normal form. Next, we illustrate that the \textbf{FNCF} of a DACS and the extended \textbf{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 \textbf{FBCF} via the explicitation procedure and a numerical example is given to show the efficiency of the proposed algorithm.

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Yahao Chen, Witold Respondek. 2021-03-27. From Morse Triangular Form of ODE Control Systems to Feedback Canonical Form of DAE Control Systems. https://doi.org/10.1016/j.jfranklin.2021.08.025

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