Noncommutative rational functions, their difference-differential calculus and realizations

被引：34
|
作者：
Kaliuzhnyi-Verbovetskyi, Dmitry S. [1 ]
Vinnikov, Victor [2 ]
机构：
[1] Drexel Univ, Dept Math, Philadelphia, PA 19104 USA
[2] Ben Gurion Univ Negev, Dept Math, IL-84105 Beer Sheva, Israel
来源：
MULTIDIMENSIONAL SYSTEMS AND SIGNAL PROCESSING | 2012年 / 23卷 / 1-2期
基金：
以色列科学基金会; 美国国家科学基金会;
关键词：
Noncommutative polynomials; Noncommutative rational functions; Skew fields of fractions; Structured noncommutative multidimensional linear systems; Noncommutative realization theory; Noncommutative difference-differential calculus; Directional derivatives; Noncommutative backward shifts; Noncommutative formal power series; MULTIDIMENSIONAL LINEAR-SYSTEMS; FORMAL POWER-SERIES; MATRIX INEQUALITIES; INFINITE SEQUENCES; UNCERTAIN SYSTEMS; OPERATORS; DILATIONS; ALGEBRAS; SPACES;
D O I：
10.1007/s11045-010-0122-3
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
Noncommutative rational functions appeared in many contexts in system theory and control, from the theory of finite automata and formal languages to robust control and LMIs. We survey the construction of noncommutative rational functions, their realization theory and some of their applications. We also develop a difference-differential calculus as a tool for further analysis.
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页码：49 / 77
页数：29
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