H2 output feedback control for discrete-time systems

This paper addresses the problem of H₂ control by output feedback for discrete-time systems. Necessary and sufficient conditions concerning the existence of a linear stabilizing output feedback gain are provided in terms of the intersection of a convex set and a set defined by a nonlinear real-valued function. The results can be easily extended to deal with linear uncertain discrete-time systems, where uncertainties are supposed to belong to convex bounded domains, providing an H₂ guaranteed cost output feedback control. Thanks to the geometric properties of the above mentioned function, numerical convex programming tools can be used in order to solve this class of H₂ control problems. Examples illustrate the theoretical results.