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This paper is concerned with the problems of delay-dependent stability and static output feedback (SOF) control of two-dimensional (2-D) discrete systems with interval time-varying delays, which are described by the Fornasini-Marchesini (FM) second model. The upper and lower bounds of delays are considered. Applying a new method of estimating the upper bound on the difference of Lyapunov function that does not ignore any terms, a new delay-dependent stability criteria based on linear matrix inequalities (LMIs) is derived. Then, given the lower bounds of time-varying delays, the maximum upper bounds in the above LMIs are obtained through computing a convex optimization problem. Based on the stability criteria, the SOF control problem is formulated in terms of a bilinear matrix inequality (BMI). With the use of the slack variable technique, a sufficient LMI condition is proposed for the BMI. Moreover, the SOF gain can be solved by LMIs. Numerical examples show the effectiveness and advantages of our results.

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This paper considers the robust guaranteed cost control problem of two‐dimensional (2‐D) state‐delayed systems. First, the definition of guaranteed cost matrix is proposed and an upper bound of the cost function is given. Then, the guaranteed cost control problem is resolved. Furthermore, the minimum upper bound of the closed‐loop cost function is obtained by solving an optimization problem with LMIs' constraints. A numerical example demonstrates the effectiveness of our results.

In this paper, we consider a class of two-dimensional (2-D) local statespace (LSS) Fornasini-Marchesini (FM) second models with delays in the states, and we study delay-independent and delay-dependent H ∞ control problems via output feedback. First, based on the definition of H ∞ disturbance attenuation γ for 2-D state-delayed systems, we propose a delay-dependent bounded real lemma. Specifically, a new Lyapunov functional candidate is introduced and free-weighting matrices are added to the difference Lyapunov functional for 2-D systems possessing two directions. Then delay-independent and delay-dependent output feedback H ∞ controllers are developed that ensure that the closed-loop system is asymptotically stable and has H ∞ performance γ in terms of linear matrix inequality (LMI) feasibility. Furthermore, the minimum H ∞ norm bound γ is obtained by solving linear objective optimization problems. Numerical examples demonstrate the effectiveness and advantages of the LMI approach to H ∞ control problems for 2-D state-delayed systems.