Direct iterative LMI-based approach of mixed H-two / H-infinity robust control for uncertain systems

Direct iterative LMI-based approach of mixed H-two/H-infinity robust control for uncertain systems YE Si-jun, WANG Xin-min, ZHANG Qing-jiang, LI Yan (School of Automation, Northwestern Polytechnical University, Xi’an Shaanxi 710129, China) Abstract: For the controller design of polytopic uncertain systems, the additional variables method is effective to reduce conservativeness. However, this method makes the dimension of linear matrix inequality (LMI) higher. Motivated by the direct iterative linear matrix inequality (DILMI) approach, a mixed H-two/H-infinity robust control method for polytopic uncertain systems is proposed. First, based on the affine quadratic stability theory, it is proved that the stability of a polytopic uncertain system can be transformed into the stability of the system at vertices of the polytope. In the light of this perspective, a sufficient condition is derived from parameter-dependent Lyapunov approach to guarantee the robust stability and mixed H-two/H-infinity performance of the polytopic uncertain system. Then, a DILMI algorithm is developed for decoupling the Lyapunov variables and the controller gain. The algorithm solves the non-convex optimization problem of the sufficient condition without introducing any additional variables. Finally, simulation results based on the F-16 polytopic model are given to demonstrate the effectiveness of the proposed method.