LMI-based criterion for the robust guaranteed cost control of 2-D systems described by the Fornasini–Marchesini second model

This paper considers the problem of the guaranteed cost control for a class of two-dimensional (2-D) discrete systems described by the Fornasini–Marchesini second local state–space (FMSLSS) model with norm-bounded uncertainties. An improved linear matrix inequality (LMI)-based criterion for the existence of robust guaranteed cost controller is established. Such controllers render the closed-loop system asymptotically stable for all admissible uncertainties and guarantee an adequate level of performance.