Optimal guaranteed cost control of 2-D discrete uncertain systems: An LMI approach

This paper addresses the problem of the optimal 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. A linear matrix inequality (LMI)-based new criterion for the existence of a state feedback controller which guarantees not only the asymptotic stability of the closed-loop system, but also an adequate performance bound over all the possible parameter uncertainties is established. Furthermore, a convex optimization problem with LMI constraints is formulated to design the optimal guaranteed cost controller which minimizes the upper bound of the closed-loop cost function.