Robust stabilization and passivity of uncertain nonlinear systems

This paper is devoted to the robust stabilization and passivity of general uncertain nonlinear systems. It is first proved that the unforced system has a unique local solution with any initial value in some neighborhood of the origin. Some properties of robust passive systems are obtained. Based on these properties, it is verified that under some conditions robust passivity of the uncertain system implies the zero-state detectability, which, together with robust passivity, can lead to robust stabilization of the uncertain nonlinear system. In addition, a C¹ state feedback controller is derived on the basis of the solution of an equation. Finally, the effectiveness of the proposed control law is demonstrated via simulations.