Stabilization of nonlinear systems by use of semidefinite Lyapunov functions (Q1961717)

The authors give a stabilizability result of the Jurdjevic-Quinn type for nonlinear, non-affine systems \[ \dot x= f(x,u), \] where \(x\in\mathbb{R}^n\), \(u\in\mathbb{R}^m\), \(f\in C^\infty\) and \(f(0,0)= 0\). The method rests on a Lyapunov function which is in general only semi-definite negative. The result is an application of a suitable extension of LaSalle's invariance principle.