$\mathcal{H}_\infty$ Control Problem for Discrete-Time Algebraic Dynamical Systems

Abstract

This paper considers the suboptimal H∞ control problem for linear discrete-time algebraic dynamical systems. Such systems can be formally described as LTI (linear and timeinvariant) discrete-time systems, whose transfer function matrix is allowed to be improper or polynomial. The parametrization of output feedback controllers is given in a realization-based setting involving two generalized algebraic Riccati equations and features the same elegant simplicity of the standard (proper) case. Two relevant numerical examples prove the effectiveness of our approach.