Finite-region dissipative control for 2-D systems in the Roesser model

Dingli Hua, Weiqun Wang and Juan Yao

International Journal of Systems Science, 2018, vol. 49, issue 16, 3406-3417

Abstract: This paper investigates the finite-region dissipative control of two-dimensional (2-D) linear discrete-time Roesser model. Firstly, we define a concept of finite-region $ (Q,S,R) $ (Q,S,R)-μ-dissipativity. Then, by using Lyapunov function and establishing special recursive formulas, a new sufficient condition with a simpler form is formulated which ensures the resulting closed-loop system is finite-region bounded. Based on this, we propose the sufficient condition for finite-region $ (Q,S,R) $ (Q,S,R)-μ-dissipativity of closed-loop system. Furthermore, the sufficient condition that can be verified by linear matrix inequalities (LMIs) for designing the finite-region $ (Q,S,R) $ (Q,S,R)-μ-dissipative state-feedback controller is given. Moreover, the finite-region passive control, finite-region $ H_\infty $ H∞ control and mixed finite-region passive and $ H_{\infty } $ H∞ control can be obtained as the special cases from the established result. Finally, numerical examples are presented to display the effectiveness of the proposed results.

Date: 2018
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DOI: 10.1080/00207721.2018.1542043

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