Canonical forms for descriptor systems under restricted system equivalence

Abstract The problem of canonical forms of implicit descriptor systems under restricted system equivalence is considered. It is shown that the canonical form is directly related to the echelon form of the autoregressive matrix inducing the external behavior of the system. The proposed canonical form is a generalization of the Popov form, and is also valid for singular systems, under transfer equivalence.

[1]  Pavol Brunovský,et al.  A classification of linear controllable systems , 1970, Kybernetika.

[2]  V. Popov.  Some properties of the control systems with irreducible matrix — Transfer functions , 1970 .

[3]  V. Kučera,et al.  Reachability and controllability indices for linear descriptor systems , 1990 .

[4]  J. Willems.  Input-output and state-space representations of finite-dimensional linear time-invariant systems , 1983 .

[5]  A Jordan control canonical form for singular systems , 1988 .

[6]  Margreta Kuijper,et al.  Descriptor representations without direct feedthrough term , 1992, Autom..

[7]  Nicos Karcanias,et al.  A Classification of Minimal Bases for Singular Systems , 1990 .

[8]  A. Morse.  Structural Invariants of Linear Multivariable Systems , 1973 .

[9]  V. Popov.  Invariant Description of Linear, Time-Invariant Controllable Systems , 1972 .

[10]  Jean Jacques Loiseau,et al.  Feedback canonical forms of singular systems , 1991, Kybernetika.

[11]  Heide Glüsing-Lüerben.  Feedback canonical form for singular systems , 1990 .

[12]  H. Rosenbrock.  Structural properties of linear dynamical systems , 1974 .

[13]  F. R. Gantmakher.  The Theory of Matrices , 1984 .

[14]  A canonical form for controllable singular systems , 1989 .

[15]  L. Mirsky,et al.  The Theory of Matrices , 1961, The Mathematical Gazette.

[16]  S. Campbell,et al.  Order and the index of singular time-invariant linar systems , 1981 .

[17]  Jean Jacques Loiseau,et al.  Proportional and proportional-derivative canonical forms for descriptor systems with outputs , 1994, Autom..

[18]  Jr. G. Forney,et al.  Minimal Bases of Rational Vector Spaces, with Applications to Multivariable Linear Systems , 1975 .