In this paper, we present a solution to the problem of non-fragile robust optimal guaranteed cost control for a class of uncertain two-dimensional(2-D) discrete systems described by the general model (GM) subject to both state and input delays. The parameter uncertainties are assumed norm-bounded. A linear matrix inequality (LMI)-based sufficient condition for the existence of non-fragile robust guaranteed cost controller is established. Furthermore, a convex optimization problem with LMI constraints is proposed to select a non-fragile robust optimal guaranteed cost controller stabilizing the uncertain 2-D discrete system with both state and input delays as well as achieving the least guaranteed cost for the resulting closed-loop system. The effectiveness of the proposed method is demonstrated with an illustrative example.

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This paper addresses the problem of non-fragile robust optimal guaranteed cost control for a class of two-dimensional discrete systems described by the general model with norm-bounded uncertainties. Based on Lyapunov method, a new linear matrix inequality (LMI)-based criterion for the existence of non-fragile state feedback controller is established. Furthermore, a convex optimization problem with LMI constraints is formulated to select a non-fragile robust optimal guaranteed cost controller, which minimizes the upper bound of the closed-loop cost function. The merit of the proposed criterion in aspect of conservativeness over a recently reported criterion is demonstrated with the help of illustrative examples.

This paper considers the problem of delay-dependent robust optimal H ∞ control for a class of uncertain two-dimensional (2-D) discrete state delay systems described by the general model (GM). The parameter uncertainties are assumed to be normbounded. A linear matrix inequality (LMI)-based sufficient condition for the existence of delay-dependent γ-suboptimal state feedback robust H ∞ controllers which guarantees not only the asymptotic stability of the closed-loop system, but also the H ∞ noise attenuation γ over all admissible parameter uncertainties is established.Furthermore, a convex optimization problem is formulated to design a delay-dependent state feedback robust optimal H ∞ controller which minimizes the H ∞ noise attenuation γ of the closed-loop system. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed method.

This paper is concerned with the problem of optimal guaranteed cost control via memory state feedback for a class of uncertain two-dimensional (2-D) discrete state-delayed systems described by the Roesser model with norm-bounded uncertainties. A linear matrix inequality (LMI)-based sufficient condition for the existence of memory state feedback guaranteed cost controllers is established and a parameterized representation of such controllers (if they exist) is given in terms of feasible solutions to a certain LMI. Furthermore, a convex optimization problem with LMI constraints is formulated to select the optimal guaranteed cost controllers that minimize the upper bound of the closed-loop cost function. The proposed method yields better results in terms of least upper bound of the closed-loop cost function as compared with a previously reported result.