An iterative convex approach for fixed-order robust ℋ2/ℋ∞ control of discrete-time linear systems with parametric uncertainty

This paper presents a convex approach to design fixed-order robust ℋ₂/ℋ_∞ controllers for discrete-time linear time-invariant (LTI) systems affected by parametric uncertainty. Starting from an a priori computed stabilizing full-order parameter-dependent controller for the same system, which is designed under the assumption that the parameter is exactly known, parameter-dependent sufficient linear matrix inequalities (LMIs) for robust ℋ₂/ℋ_∞ analysis and synthesis are presented. A novel LMI procedure is proposed to iteratively compute less conservative robust controllers, utilizing a feasible solution of the fixed-order synthesis conditions as a starting point. Assuming polynomial parameter dependencies of all system matrices, tractable LMI formulations that guarantee feasibility of the parameter-dependent conditions are derived using well-known relaxations based on Pólya´s theorem. Numerical comparisons with existing methods confirm the potential of the proposed robust controller design approach.