Robust static and fixed-order dynamic output feedback control of discrete-time parametric uncertain Luré systems: Sequential SDP relaxation approaches

Design methods are proposed for static and fixed‐order dynamic output feedback controllers for discrete‐time Luré systems with sector‐bounded nonlinearities in the presence of parametric uncertainties described by polytopes. The derived design conditions are represented in terms of bilinear matrix inequalities, which are nonconvex. By using convex relaxation methods, controller design equations are derived for systems with multiple states, outputs, and nonlinearities in terms of linear matrix inequalities (LMIs) and iterative LMIs, which are associated with semidefinite programs. The proposed design methods are developed from stability conditions using parameter‐dependent Lyapunov functions, and existing iterative numerical methods are adapted to solve certain classes of nonconvex optimization problems for controller design. Several numerical examples are provided to illustrate and verify the proposed design methods.