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

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 $(Q,S,R)$-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 $(Q,S,R)$-μ-dissipativity of closed-loop system. Furthermore, the sufficient condition that can be verified by linear matrix inequalities (LMIs) for designing the finite-region $(Q,S,R)$-μ-dissipative state-feedback controller is given. Moreover, the finite-region passive control, finite-region $H_{\mathrm{\infty }}$ control and mixed finite-region passive and $H_{\mathrm{\infty }}$ 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.

KEYWORDS:

• Finite-region boundedness
• finite-region dissipativity
• 2-D Roesser model
• linear matrix inequalities

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by National Natural Science Foundation of China (Grant nos. 61573007 and 61603188).