ISSN:
1573-0824
Keywords:
2D system
;
polynomial matrices
;
unilateral equation
;
Bezout equation
;
Gröbner basis
;
module
;
output feedback
;
stabilizability
;
stabilization
Source:
Springer Online Journal Archives 1860-2000
Topics:
Electrical Engineering, Measurement and Control Technology
Notes:
Abstract Alternative methods are proposed for test of output feedback stabilizability and construction of a stable closed-loop polynomial for 2D systems. By the proposed methods, the problems can be generally reduced to the 1D case and solved by using 1D algorithms or Gröbner basis approaches. Another feature of the methods is that their extension to certain specialnD (n〉2) cases can be easily obtained. Moreover, the “Rabinowitsch trick,” a technique ever used in showing the well-known Hilbert's Nullstellensatz, is generalized in some sense to the case of modules over polynomial ring. These results eventually lead to a new solution algorithm for the 2D polynomial matrix equationD(z, w)X(z, w)+N(z, w)Y(z, w)=V(z, w) withV(z, w) stable, which arises in the 2D feedback design problem. This algorithm shows that the equation can be effectively solved by transforming it to an equivalent Bezout equation so that the Gröbner basis approach for polynomial modules can be directly applied.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00985862
