Robust stabilization for single-input polytopic nonlinear systems

This work deals with the stabilization problem of single-input polytopic nonlinear systems. The uncertain parameters in the systems can be time-varying. The control Lyapunov function approach is used to derive a sufficient condition for the existence of time-invariant, continuous, asymptotically stabilizing state feedback controllers. Additionally, a universal formula for constructing stabilizing controllers when the obtained sufficient condition is met is presented. For some polytopic linear systems, it is proved that the sufficient condition can be equivalently expressed in terms of linear matrix inequality (LMI) formulation. Moreover, the obtained stabilizing controllers can be linear. Simulation results confirm the effectiveness of the design.