TY - JOUR
T1 - Approach to simultaneous system design
T2 - Part II. Nonswitching gain and dynamic feedback compensation by algebraic geometric methods
AU - Ghosh, Bijoy K.
N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 1988
Y1 - 1988
N2 - This paper studies structured uncertainty problems in feedback system design, considers a compact parameterization of the space of linear dynamical systems and introduces 'base points' and 'critical points' as two algebraic-geometric objects that have significance in sensitivity and robustness studies, respectively. Using the Nevanlinna-Pick interpolation theory, the author obtains a necessary and sufficient condition for simultaneous stabilization of a structured one-parameter family of plants. A recent result due to Kharitonov, on the simultaneous stability of a parameterized family of polynomials, leads to a sufficiency condition for simultaneous stabilization of a structured multiparameter family of plants. The author considers 'simultaneous pole placement' of an r-tuple of plants as a means to arbitrarily tune the natural frequencies of a multimode linear dynamical system. The concept of 'nondegenerate' and 'twisted' r-tuples of plants is introduced as the pole placement problem is studied via Schubert enumerative geometry as an intersection problem on the associated Grassmannian. Other design problems, viz., the strong stabilization problem and the dead beat control problem, are also considered.
AB - This paper studies structured uncertainty problems in feedback system design, considers a compact parameterization of the space of linear dynamical systems and introduces 'base points' and 'critical points' as two algebraic-geometric objects that have significance in sensitivity and robustness studies, respectively. Using the Nevanlinna-Pick interpolation theory, the author obtains a necessary and sufficient condition for simultaneous stabilization of a structured one-parameter family of plants. A recent result due to Kharitonov, on the simultaneous stability of a parameterized family of polynomials, leads to a sufficiency condition for simultaneous stabilization of a structured multiparameter family of plants. The author considers 'simultaneous pole placement' of an r-tuple of plants as a means to arbitrarily tune the natural frequencies of a multimode linear dynamical system. The concept of 'nondegenerate' and 'twisted' r-tuples of plants is introduced as the pole placement problem is studied via Schubert enumerative geometry as an intersection problem on the associated Grassmannian. Other design problems, viz., the strong stabilization problem and the dead beat control problem, are also considered.
UR - http://www.scopus.com/inward/record.url?scp=0024035929&partnerID=8YFLogxK
U2 - 10.1137/0326051
DO - 10.1137/0326051
M3 - Article
AN - SCOPUS:0024035929
VL - 26
SP - 919
EP - 963
JO - SIAM Journal on Control and Optimization
JF - SIAM Journal on Control and Optimization
SN - 0363-0129
IS - 4
ER -