A Nonlinear Gain-Scheduling Compensation Approach Using Parameter-Dependent Lyapunov Functions

This paper addresses the gain-scheduling control design for nonlinear systems to achieve output regulation. For gain-scheduling control, the linear parameter-varying (LPV) model is obtained by linearizing the plant about zero-error trajectories upon which an LPV controller is based. A key in this process is to find a nonlinear output feedback compensator such that its linearization matches with the designed LPV controller. Then, the stability and performance properties of LPV control about the zero-error trajectories can be inherited when the nonlinear compensator is implemented. By incorporating the exosystem, nominal input, and measured output information into the LPV model, the LPV control synthesis problem is formulated as linear matrix inequalities (LMIs) using parameter-dependent Lyapunov functions (PDLFs). Moreover, explicit formulae for the construction of the nonlinear gain-scheduled compensator have been derived to meet the linearization requirement. Finally, the validity of the proposed nonlinear gain-scheduling control approach is demonstrated through a ball and beam example.