The notion of V-detectability and stabilization of invariant sets of nonlinear systems

The problem of global (local) stabilizability of an invariant set of passive nonlinear controlled system is considered. New notion of detectability of the zero value set of a storage function is introduced. It is shown that this property plays a fundamental role in solving of invariant set stabilization problems and in defining the global (local) stabilizing regulator. Sufficient conditions, implying that passive nonlinear system has a detectable zero value set for a smooth storage function, are proposed.