Reliable algorithms for computing minimal dynamic covers

Minimal dimension dynamic covers play an important role in solving the structural synthesis problems of minimum order functional observers or fault detectors, or in computing minimal order inverses or minimal degree solutions of rational equations. We propose numerically reliable algorithms to compute two basic types of minimal dimension dynamic covers for a linear system. The proposed approach is based on a special controllability staircase condensed form of a structured pair (A, [B/sub 1/, B/sub 2/]), which can be computed using exclusively orthogonal similarity transformations. Using such a condensed form minimal dimension covers and corresponding feedback/feedforward matrices can be easily computed. The overall algorithm has a low computational complexity and is provably numerically reliable.

[1]  Andras Varga,et al.  Reliable algorithms for computing minimal dynamic covers for descriptor systems , 2004 .

[2]  Karsten P. Ulland,et al.  Vii. References , 2022 .

[3]  A. Varga.  On computing least order fault detectors using rational nullspace bases , 2003 .

[4]  A. Morse,et al.  Feedback invariants of linear multivariable systems , 1972 .

[5]  Andras Varga.  New computational approach for the design of fault detection and isolation filters , 2004 .

[6]  Keith Glover,et al.  Generalized dynamic covers for linear systems with applications to deterministic identification and realization problems , 1976, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

[7]  L. Silverman,et al.  Minimal dynamic inverses for linear systems with arbitrary initial states , 1976 .

[8]  A. Laub,et al.  The singular value decomposition: Its computation and some applications , 1980 .

[9]  A. Varga.  Numerically stable algorithm for standard controllability form determination , 1981 .

[10]  A. S. Morse,et al.  Minimal solutions to transfer matrix equations , 1976 .

[11]  Andras Varga.  Computation of Kalman decompositions of periodic systems , 2003, ECC.

[12]  Hidenori Kimura,et al.  Geometric structure of observers for linear feedback control laws , 1977 .

[13]  András Varga,et al.  Computation of irreducible generalized state-space realizations , 1990, Kybernetika.

[14]  A. Varga.  A Schur method for pole assignment , 1981 .

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

[16]  C. Paige.  Properties of numerical algorithms related to computing controllability , 1981 .

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

[18]  P. Dooren.  The generalized eigenstructure problem in linear system theory , 1981 .