H-infinity control problem for general discrete-time systems

Abstract: The paper considers the suboptimal H-infinity control problem for a general discrete-time system (whose transfer function matrix is allowed to be improper or polynomial). The parametrization of output feedback controllers is given in a realization-based setting, involves two generalized algebraic Riccati equations, and features the same elegant simplicity of the standard (proper) case. A relevant real-life numerical example proves the effectiveness of our approach.