Performance control of rational systems using linear-fractional representations and LMIs

Every nonlinear system of the rational type admits a “linear-fractional representation” (LFR), which consists of an LTI system connected with a diagonal feedback operator linear in the state. Using this representation, the authors can compute a quadratic Lyapunov function that proves various properties for the system (stability of a polytope of initial conditions, L₂-induced gain, etc.). These properties are checked by solving a convex optimization problem over linear matrix inequalities (LMIs). The approach can be used for state-feedback synthesis, and also for dynamic output-feedback synthesis, provided the state equations are linear in every state coordinate that is not measured