Smooth output feedback stabilization for nonlinear systems with time-varying powers

This paper considers the global asymptotic stabilization problem for a class of nonlinear systems with time-varying powers. With only upper and lower bounds of the time-varying power, a smooth state feedback control law solving the problem is frst developed via the so-called adding a power integrator technique. When the system state is not fully available and the time-varying power is exactly known, a smooth output feedback control law constituted by a nonlinear state observer and a state feedback is constructed for achieving the stabilization task. In both cases, systematic approaches are explicitly presented for designing gains of control law and observer.