Improving nonlinear control performance with a hybrid control strategy

To overcome inadequate performance behavior of nonlinear stabilizing control law derived from standard backstepping design, we propose a hybrid control approach to robustly stabilizing polynomial nonlinear systems in a global sense as well as improving the system performance in a local region. Specifically, we keep using backstepping controller in large space until the state trajectories entering a small region around the origin. Within the bounded region the states will be treated as parameter variables and the nonlinear system is reasonably represented as an LPV system. The construction of LPV state feedback control law together with the states/region boundedness characterization are expressed as semi-definite programming problems, and solved using SOS programming techniques. As shown by an example, the proposed hybrid controller not only maintains the system robustness but also enhances the performance by providing smaller L₂ gain and faster convergence rate.