Robust output feedback controller design via genetic algorithms and LMIs: the mixed / Hscr/(2)// Hscr// / infin// problem

This paper deals with the mixed / Hscr/(2)// Hscr// / infin// control problem for uncertain continuous-time linear systems. The polytopic parametric uncertainties are studied. Based on genetic algorithms (GAs) and linear matrix inequalities (LMIs), a hybrid algorithm is presented for numerical computation of an optimal fixed-order static or dynamic output feedback robust controller. The genetic algorithm is used to obtain the population of controllers and the LMI based routines are used to minimize some performance criterion. The problem is formulated in terms of different Lyapunov functions. This approach can be used for synthesis of reduced or full-order controllers. Some examples borrowed from the literature are discussed to illustrate and validate this approach.