An LMI optimization approach to multiobjective controller design for discrete-time systems

In this paper we investigate the design of multiobjective controllers for linear discrete-time systems. We show that, as for the H/sub 2/ norm, it is possible to extend the linear matrix inequality (LMI) characterization of the H/sub /spl infin// norm condition so that it no longer exhibits the product of the Lyapunov matrix and the system dynamic matrices. Then we develop a parametrization for state-feedback and output-feedback linear controllers which linearizes these extended H/sub 2/ and H/sub /spl infin// norm conditions for synthesis. These parametrizations are applied to the design of controllers with multiobjective constraints. A numerical example illustrates the results and provide a comparison with some of the existing methods.