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

Abstract

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 ∞ 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.