H∞ model approximation for uncertain stochastic systems: Discrete-time case

This paper is concerned with the problem of H∞ model approximation for discrete time systems that possess uncertain stochastic and time delay dependent parameters. In order to get a stable system, our attention is focused on the construction of reduced-order models, which guarantee the corresponding error system to be asymptotically stable and have a prescribed H∞ error performance. Sufficient conditions for the solvability of the problem is obtained via linear matrix inequalities (LMIs) and a coupling non-convex rank constraint set. An explicit parametrization of the desired reduced-order models is presented when these conditions are satisfied. Finally, a numerical example is given to illustrate the effectiveness of the proposed theories.