From Morse triangular form of ODE control systems to feedback canonical form of DAE control systems

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