Title :
2-D version of Bellman-Gronwall lemma
Author :
Fan, Huijin ; Wen, Changyun
Author_Institution :
Sch. of Electr. & Electron. Eng., Nanyang Technol. Univ., Singapore
Abstract :
In the one-dimensional (1D) case, Bellman-Gronwall Lemma plays an important role in the field of system theory. For example, it is a key technique in analyzing the shift-variant systems and adaptive systems. But there is no such result available in the two-dimensional (2D) case. In this paper, we first establish a simplified version of 2D counterpart of the Bellman-Gronwall Lemma for its potential application in analyzing 2D shift-variant systems and adaptive systems. Then a general version of 2D Bellman-Gronwall Lemma is derived by a 2D inductive method. These results are analogical to the 1D Bellman-Gronwall Lemma.
Keywords :
adaptive systems; differential equations; multidimensional systems; stability; 2D inductive method; 2D shift-variant systems; Bellman-Gronwall lemma; adaptive systems; shift-variant systems; system theory; Adaptive control; Adaptive systems; Algebra; Control systems; Differential equations; Programmable control; Robust control; Robust stability; Stability analysis; Two dimensional displays;
Conference_Titel :
Control, Automation, Robotics and Vision, 2002. ICARCV 2002. 7th International Conference on
Print_ISBN :
981-04-8364-3
DOI :
10.1109/ICARCV.2002.1238575
