Block decoupling invariants: Geometric and transfer matrix characterizations

In this paper we consider the block decoupling problem with stability for linear time invariant systems in the general case i.e. the system transfer matrix is not supposed to be surjective. The aim of this work is twofold, first to introduce new lists of invariants called the “stable block essential structures” of the system and then to provide several equivalent characterizations of these invariants within both transfer matrix and geometric approaches.

[1]  A. Morse.  System Invariants under Feedback and Cascade Control , 1976 .

[2]  R. Brockett,et al.  The reproducibility of multivariable systems , 1964 .

[3]  W. Wonham.  Linear Multivariable Control: A Geometric Approach , 1974 .

[4]  J. Dion,et al.  New feedback invariants and the block decoupling problem , 1990 .

[5]  G. Verghese.  Infinite-frequency behaviour in generalized dynamical systems , 1978 .

[6]  J. Descusse,et al.  New decoupling invariants: the essential orders , 1986 .

[7]  William A. Wolovich,et al.  On the synthesis of multivariable systems , 1973 .

[8]  W. M. Wonham,et al.  Linear Multivariable Control , 1979 .

[9]  J. Dion,et al.  Invariant spaces at infinity of linear systems application to block decoupling , 1990 .

[10]  Brian D. O. Anderson,et al.  Triangularization technique for the design of multivariable control systems , 1978 .

[11]  J. A. Torres,et al.  Minimal structure in the block decoupling problem with stability , 1991, Autom..

[12]  M. Heymann,et al.  Linear feedback decoupling--Transfer function analysis , 1983 .

[13]  J. Descusse,et al.  Solution to Morgan's problem , 1988 .

[14]  M. Heymann,et al.  Linear Feedback—An Algebraic Approach , 1978 .

[15]  J. Dion,et al.  The minimal delay decoupling problem: feedback implementation with stability , 1988 .

[16]  J. Descusse,et al.  On the structure at infinity of linear square decoupled systems , 1982 .

[17]  J. Dion,et al.  Some factorizations at infinity of rational matrix functions and their control interpretation , 1982 .

[18]  Thomas Kailath,et al.  Linear Systems , 1980 .

[19]  C. Desoer,et al.  Multivariable Feedback Systems , 1982 .

[20]  Nicos Karcanias,et al.  Structure, Smith-MacMillan form and coprime MFDs of a rational matrix inside a region P =ω∪{∞} , 1983 .