Stabilization of a class of multi-inputs nonlinear systems
The authors investigate the local stabilization of an affine system \(\dot x= f(x)+ \sum^{n-1}_{n=1} u_ i g_ i(x)\) by means of state feedback. First, they gave a sufficient and necessary condition, which is that Lie algebra, Lie \((g_ 1,\dots, g_{n-1})\), generated by \(g_ 1,\dots,g_{n-1}\), has a constant dimension, for an affine system to be feedback equivalent to the reduced system \(\dot x_ 1- f(x_ 1, x_ 2)\), \(\dot x_ 2=v\), \((x_ 1,x_ 2)\in \mathbb{R}^{n-m} \times\mathbb{R}^ m\), where \(v\) is a control vector. Next, using the above idea they provide the conditions, under which the above reduced system is stabilizable. Furthermore, they present the feedback to stabilize the above-mentioned system.
scientific article; zbMATH DE number 612401