Noncommutative rational functions, their difference-differential calculus and realizations

作者：Kaliuzhnyi Verbovetskyi Dmitry S^*; Vinnikov Victor

来源：Multidimensional Systems and Signal Processing, 2012, 23(1-2): 49-77.

DOI：10.1007/s11045-010-0122-3

• 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

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.

• 出版日期2012-6