Angular metric and its application in multi-model robust control of nonlinear systems

A new metric, angular metric, is defined in the linear space of real rational matrices, which can measure the uncertainties and describe the performance specifications of the robust control system. In the framework of this metric, robust stability margin is defined to characterize the stability robustness of the closed-loop system, which is proposed to calculate the weighting coefficients in multi-linear model approach used to control a strongly nonlinear system. Reasonable operation points for nonlinear system are selected to design the corresponding optimal robust compensator. Then the global robust controller is built from a weighted combination of local controllers whose outputs are weighted by the robust stability margin. A highly nonlinear example is introduced to indicate that the designed control system has good performance for nonlinear system.