Global regulation for nonlinear systems (Q2745625)

The global regulation of the system NEWLINE\[NEWLINE\begin{aligned} \dot x & = f(x,w,u),\\ \dot w & = r(w)\\ e & =h(x,w)\end{aligned}NEWLINE\]NEWLINE is shown to be solvable by state feedback iff there exist mappings \(c,S\) such that NEWLINE\[NEWLINE\begin{aligned} {\partial S(w) \over \partial w}r(w) & = f\bigl(S(w),w,c(w)\bigr),\;w\in\mathbb{R}^r\\ h\bigl(S(w), w\bigr) & =0.\end{aligned}NEWLINE\]NEWLINE This generalises the local result of Isidori and Byrnes.