A remark on Lagrange stability of nonlinear systems stabilization (Q1195668)

The problem of stability (in the sense of Lagrange) for nonlinear control systems is considered. For simplificity only the single input-single output systems are treated. It is proved under suitable assumptions, that if there is a bounded input \(u\) such that the corresponding output is bounded for any initial condition, then the system is \(u\)-Lagrange stable. Furthermore, some assumptions are proposed under which the Lagrange stability with respect to any bounded input implies existence of a stability feedback law.