Algorithm 718: A FORTRAN subroutine to solve the eigenvalue allocation problem for single-input systems

ABSTRACT

An efficient implementation of an algorithm for the eigenvalue allocation (pole placement) problem of single-input linear systems using state feedback is given in this paper. The implementation uses the BLAS level-1 [2] subroutines when possible for better performance. A brief description of the algorithm along with some computational details is also given.

REFERENCES

• 1: W. J. Cody, Algorithm 665: Machar: a subroutine to dynamically determined machine parameters, ACM Transactions on Mathematical Software (TOMS), v.14 n.4, p.303-311, Dec. 1988 [doi>10.1145/50063.51907]
• 2: C. L. Lawson , R. J. Hanson , D. R. Kincaid , F. T. Krogh, Basic Linear Algebra Subprograms for Fortran Usage, ACM Transactions on Mathematical Software (TOMS), v.5 n.3, p.308-323, Sept. 1979 [doi>10.1145/355841.355847]
• 3: LUENBERGER, D.G. Introduction to Dynamzc Systems Theory, Models and Apphcatzons, John Wiley and Sons, New York, 1979.
• 4: GARBOW, t3. S., BO~q~E, J. M., DONC~^RRA, J J., AND MOLE~, C. B. Matrix Elgensystem Routi,es: EISPACK Guide Extension. Springer-Verlag, 1972.
• 5: W. Morven Gentleman , Scott B. Marovich, More on algorithms that reveal properties of floating point arithmetic units, Communications of the ACM, v.17 n.5, p.276-277, May 1974 [doi>10.1145/360980.361003]
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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.3 Numerical Linear Algebra
          Subjects: Eigenvalues and eigenvectors (direct and iterative methods)

Additional Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.1 Numerical Algorithms and Problems
          Subjects: Computations on matrices

  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.0 General
          Subjects: Numerical algorithms

General Terms:
Algorithms

Keywords:
deflation, eigenvalue allocation, numerical efficiency, pole placement