Pole-zero representation of descriptor systems

We present an algorithm for computing the pole-zero representation of descriptor systems whose generalized state-space models are described by the 5-tuple (E, A, b, c. d), where E may be a singular matrix but del (A - λE) ? 0. The proposed algorithm uses only-orthogonal transformations; hence the computed results are numerically reliable. Numerical examples are included to illustrate the proposed results.

[1]  R. W. Newcomb,et al.  Degenerate networks , 1966 .

[2]  T. Kailath,et al.  A generalized state-space for singular systems , 1981 .

[3]  Paul Van Dooren,et al.  Computation of structural invariants of generalized state-space systems , 1994, Autom..

[4]  Andras Varga,et al.  Numerically stable algorithm for transfer function matrix evaluation , 1981 .

[5]  G. Stewart,et al.  An Algorithm for Generalized Matrix Eigenvalue Problems. , 1973 .

[6]  Michel Verhaegen,et al.  On the use of unitary state-space transformations , 1985 .

[7]  P. Bernhard On Singular Implicit Linear Dynamical Systems , 1982 .

[8]  C. Pan,et al.  Rank-Revealing QR Factorizations and the Singular Value Decomposition , 1992 .

[9]  H. Rosenbrock,et al.  State-space and multivariable theory, , 1970 .

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

[11]  Jk Sridhar,et al.  Computation of transfer function matrices , 1985 .

[12]  T. Kailath,et al.  Properties of the system matrix of a generalized state-space system , 1980, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[13]  D. Luenberger Dynamic equations in descriptor form , 1977 .

[14]  Rajnikant V. Patel,et al.  Computation of minimal-order realizations of generalized state-space systems , 1989 .

[15]  A. Varga,et al.  Computation of transfer-function matrices of generalized state-space models , 1989 .

[16]  Gene H. Golub,et al.  Matrix computations , 1983 .

[17]  P. Dooren The Computation of Kronecker's Canonical Form of a Singular Pencil , 1979 .

[18]  F. Lewis A survey of linear singular systems , 1986 .

[19]  P. Misra,et al.  Computation of transfer function matrices of linear multivariable systems , 1987, Autom..

[20]  C. Desoer,et al.  Degenerate networks and minimal differential equations , 1975 .

[21]  G. Miminis Deflation in eigenvalue assignment of descriptor systems using state feedback , 1993, IEEE Trans. Autom. Control..

[22]  Alan J. Laub,et al.  The linear-quadratic optimal regulator for descriptor systems , 1985, 1985 24th IEEE Conference on Decision and Control.

[23]  D. Cobb Controllability, observability, and duality in singular systems , 1984 .

[24]  T. Chan Rank revealing QR factorizations , 1987 .

[25]  A. Laub,et al.  The linear-quadratic optimal regulator for descriptor systems , 1987 .

[26]  P. Misra Hessenberg-triangular reduction and transfer function matrices of singular systems , 1989 .