Global asymptotic stabilization of general nonlinear systems with stable free dynamics via passivity and bounded feedback (Q1923076)

The Jurdjevic-Quinn method and its generalizations provide a useful tool for local and global asymptotic stabilization of nonlinear affine systems whose drift terms are Lyapunov stable. In this paper, the author considers non-affine systems of the general form \(\dot x=f(x,u)\) under the assumptions that the unforced system \(\dot x=f(x,0)\) is Lyapunov stable, and that a proper, smooth Lyapunov function \(V(x)\) such that \(L_{f(x,0)}V(x)\leq 0\), for all \(x\in\mathbb{R}^n\), is available. By exploiting the concepts of passivity, feedback equivalence and the technique of bounded state feedback, as well as some Lie algebraic conditions, the author obtains sufficient conditions for global asymptotic stability by state and dynamic output feedback. The expression of the stabilizing feedback law is explicit.