Decoupling and feedback stabilization for nonlinear differential-algebraic control systems (Q2726076)

In the paper the authors consider the problems of decoupling and feedback stabilization for the following nonlinear differential-algebraic control system: NEWLINE\[NEWLINE\begin{matrix} \dot{x}=f_{11}(x)+f_{12}(x)v+g(x)u, \\ 0=f_{21}(x)+f_{22}(x)v+h(x)u, \\ y=m(x)+n(x)v, \end{matrix}NEWLINE\]NEWLINE where \(x\in {\mathbb R}^n\) is the state, \(v\in {\mathbb R}^m\) is the limited input, \(u\in {\mathbb R}^p\) is the control input, and \(y\) is the output. They present a condition under which the system can be decoupled with a feedback controller, and then this result is proved. Moreover, a stabilizing feedback control law is presented.