Global stabilization by output dynamic feedback for triangular systems (Q1295133)

The systems considered in this paper are in single input, triangular form \[ \begin{cases} \dot x = f(x,y_1)\\ \dot y_1=y_2+g_1(x,y_1)\\ \dot y_2=y_3+g_2(x,y_1,y_2)\\ \hdotsfor 1\\ \dot y_m+y_{m+1}+g_m(x,y_1,\dots,y_m)\end{cases} \] where \(x\in\mathbb{R}^n\). The variables \(y_{m+1}\) and \(y_1\) play respectively the roles of the input and the output. The author proves that if the subsystem \(\dot x = f(x,v)\) is ISS-stable and some extra conditions are satisfied by the functions \(f,g_1,\dots,g_m\), then the system is stabilizable by dynamic output feedback.