Some aspects in l1-gain control of positive 2-D systems in Roesser model with directional delays.
Người báo cáo: PGS. TS. Lê Văn Hiện (Khoa Toán-Tin, Đại học Sư phạm Hà Nội)

Thời gian: 9h30 ngày 30 tháng 11 năm 2021

Link seminar: https://meet.google.com/gre-ofgc-oio?pli=1&authuser=1

Tóm tắt: This paper is concerned with the problems of performance analysis and synthesis of l1-gain control two-dimensional (2-D) positive Roesser systems with directional delays. By exploiting a new approach based on 2-D Z-transform, a characterization of l1-induced norm of the input-output operator is obtained. This analytical result is utilized to derive necessary and sufficient conditions under which a 2-D positive system with delays is asymptotically stable with a prescribed l1-gain performance. Then, based on a vertex optimization approach, necessary and sufficient conditions are established for the existence of a state-feedback controller that makes the closed-loop system positive and stable subject to l1-induced performance. The proposed synthesis conditions are formulated in terms of linear programming problems, which can be effectively solved by various convex algorithms to minimize the l1-performance index.