Bilinear model approximation for a class of regionally stable uncertain nonlinear systems

This paper proposes a convex approach to the model approximation problem for a class of regionally stable uncertain nonlinear systems. More specifically, we determine an extended bilinear system which approximates in a given region of the state space the input-to-output dynamics of the nonlinear system with time-varying parameters. To this end, we use a suitable parametrization of the Lyapunov matrix in order to obtain convex model design conditions in terms of linear matrix inequalities (LMIs). The proposed approach is also extended to the model reduction case without rank constraints.