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.
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This work was supported in part by the National Natural Science Foundation of China (60525303 and 60604004), NSF of Hebei Province (08M008) and the Key Scientific Research Project of the Education Ministry (204014).
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Peng, D., Guan, X. Output Feedback H ∞ Control for 2-D State-Delayed Systems. Circuits Syst Signal Process 28, 147–167 (2009). https://doi.org/10.1007/s00034-008-9074-3
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DOI: https://doi.org/10.1007/s00034-008-9074-3