From Morse triangular form of ODE control systems to feedback canonical form of DAE control systems. Issue 16 (October 2021)

• Record Type: Journal Article
• Authors: Chen, Yahao; Respondek, Witold
• Is Part Of: Journal of the Franklin Institute. Volume 358:Issue 16(2021)
• Page Start: 8556
• Page End: 8592
• Publication Date: 2021-10
• Subjects: Science -- Periodicals; Technology -- Periodicals; Patents -- United States -- Periodicals; 505
• DOI: 10.1016/j.jfranklin.2021.08.025
• Languages: English
• ISSNs: 0016-0032

Abstract

Abstract: 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.