Extended linear matrix inequality approach to multiobjective output feedback controller design

In this paper, a new linear matrix inequality approach to the multiobjective controller synthesis for continuous-time linear systems is presented. This new synthesis procedure is investigated for the dynamic output feedback controllers. Our approach is based on the newly developed extended norm characterizations which exhibits a kind of decoupling between the Lyapunov and the system matrices. In this paper, we develop a parameterization for output-feedback linear controllers which linearizes the extended norm conditions for synthesis of controller parameters. These extended synthesis linear matrix inequalities are less conservative in comparison to the previously presented counterparts since the optimization variables associated with the controller parameters are independent of the symmetric Lyapunov matrix. This feature is significant due to the several reasons. First, parameter dependent Lyapunov function can be considered which could provide a very positive impact on the design of robust control problems. Second, the design of controller with mixed objectives such as H₂ performance and H_infinperformance can be addressed without employing a unique Lyapunov matrix while still the controller design amounts to solving a set of linear matrix inequalities. The validity of this approach is illustrated by a design example.