A Nonlinear Gain Scheduling Compensation Approach Using Parameter Dependent Lyapunov Functions

Abstract

This paper addresses the gainscheduling control design for nonlinear systems to achieve output regulation. For gainscheduling control, the linear parametervarying (LPV) model is obtained by linearizing the plant about zeroerror 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 zeroerror 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 parameterdependent Lyapunov functions (PDLFs). Moreover, explicit formulae for the construction of the nonlinear gainscheduled compensator have been derived to meet the linearization requirement. Finally, the validity of the proposed nonlinear gainscheduling control approach is demonstrated through a ball and beam example.