✦ LIBER ✦

The companion matrix and Liapunov functions for linear multivariable time-invariant systems

✍ Scribed by Henry M. Power

Publisher: Elsevier Science
Year: 1967
Tongue: English
Weight: 1022 KB
Volume: 283
Category: Article
ISSN: 0016-0032
DOI: 10.1016/0016-0032(67)90025-7

No coin nor oath required. For personal study only.

✦ Synopsis

An algorithm is developed to generate a class of matrices N which, when nonsingular, red& a co&a@ square matrix A by a kmilarit~ transfomnation C = NAN-l to the Cwnpanion form. The coeficients of the characteristic equation 1 s1 -A 1 = 0 are dkplayed in the last row of C: stability of the multivariable system % = AX may thus be determined by the Routh-Hurwits procedure. If the system is stable, Liapunov functions may be genwated by further transformation of C to Routh or Sch.warz canonical forms. The former is particularly useful for calculation of quadratic furdionuls of the response stemming from non-zero initial conditions x(O) I The algorithm is used to produce a generalized Vandermonde matrix which relates a companion m&ix with repeated eigenvalues to the Jordati canonical form.

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