Output Feedback H∞ Control for 2-D State-Delayed Systems

In this paper, we consider a class of two-dimensional (2-D) local state-space (LSS) Fornasini-Marchesini (FM) second models with delays in the states, and we study delay-independent and delay-dependent H (az) control problems via output feedback. First, based on the definition of H (az) disturbance attenuation gamma 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 (az) controllers are developed that ensure that the closed-loop system is asymptotically stable and has H (az) performance gamma in terms of linear matrix inequality (LMI) feasibility. Furthermore, the minimum H (az) norm bound gamma is obtained by solving linear objective optimization problems. Numerical examples demonstrate the effectiveness and advantages of the LMI approach to H (az) control problems for 2-D state-delayed systems.