Two-Dimensional Dissipative Control and Filtering for Roesser Model

• Published in: IEEE transactions on automatic control Vol. 60; no. 7; pp. 1745 - 1759
• Main Authors: Ahn, Choon Ki, Shi, Peng, Basin, Michael V.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.07.2015; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: control and filtering; Dissipativity; Educational institutions; Integrated circuits; Interconnected systems; Linear matrix inequalities; Stability analysis; Symmetric matrices; Two dimensional displays; two-dimensional (2-D) system; two-dimensional (2-D) system; dissipativity; Control and filtering; Roesser model
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2015.2398887

This paper investigates the problems of two-dimensional (2-D) dissipative control and filtering for a linear discrete-time Roesser model. First, a novel sufficient condition is proposed such that the discrete-time Roesser system is asymptotically stable and 2-D (Q, S, R)-α-dissipative. Special cases, such as 2-D passivity performance and 2-D H ∞ performance, and feedback interconnected systems are also discussed. Based on this condition, new 2-D (Q, S, R)-α-dissipative state-feedback and output-feedback control problems are defined and solved for a discrete-time Roesser model. The design problems of 2-D (Q, S, R)-α-dissipative filters of observer form and general form are also considered using a linear matrix inequality (LMI) approach. Two examples are given to illustrate the effectiveness and potential of the proposed design techniques.