Hybrid differential evolution method for the mixed H 2 / H ∞ robust control problem under pole assignment

This paper is concerned with the mixed H2/H∞ control problem combined with robust pole placement in linear matrix inequality (LMI) regions. Based on Differential Evolution algorithms (DEs), Salomon’s Evolutionary Gradient Search method (EGS) and LMIs, a hybrid algorithm is presented for numerical computation of a robust fixed-order, static or dynamic, output feedback controller. This approach does not require that all specifications are enforced by a single closed-loop Lyapunov function. This allows to reduce the conservatism of the usual existing methods. This approach can be used for synthesis of reduced or full order controllers. Examples borrowed from the literature are discussed to validate this approach.