Purpose
To check stability/antistability of finite eigenvalues with respect to a given stability domain.Specification
SUBROUTINE AB09JX( DICO, STDOM, EVTYPE, N, ALPHA, ER, EI, ED,
$ TOLINF, INFO )
C .. Scalar Arguments ..
CHARACTER DICO, EVTYPE, STDOM
INTEGER INFO, N
DOUBLE PRECISION ALPHA, TOLINF
C .. Array Arguments ..
DOUBLE PRECISION ED(*), EI(*), ER(*)
Arguments
Mode Parameters
DICO CHARACTER*1
Specifies the type of the stability domain as follows:
= 'C': for a continuous-time system;
= 'D': for a discrete-time system.
STDOM CHARACTER*1
Specifies whether the domain of interest is of stability
type (left part of complex plane or inside of a circle)
or of instability type (right part of complex plane or
outside of a circle) as follows:
= 'S': stability type domain;
= 'U': instability type domain.
EVTYPE CHARACTER*1
Specifies whether the eigenvalues arise from a standard
or a generalized eigenvalue problem as follows:
= 'S': standard eigenvalue problem;
= 'G': generalized eigenvalue problem;
= 'R': reciprocal generalized eigenvalue problem.
Input/Output Parameters
N (input) INTEGER
The dimension of vectors ER, EI and ED. N >= 0.
ALPHA (input) DOUBLE PRECISION
Specifies the boundary of the domain of interest for the
eigenvalues. For a continuous-time system
(DICO = 'C'), ALPHA is the boundary value for the real
parts of eigenvalues, while for a discrete-time system
(DICO = 'D'), ALPHA >= 0 represents the boundary value for
the moduli of eigenvalues.
ER, EI, (input) DOUBLE PRECISION arrays, dimension (N)
ED If EVTYPE = 'S', ER(j) + EI(j)*i, j = 1,...,N, are
the eigenvalues of a real matrix.
ED is not referenced and is implicitly considered as
a vector having all elements equal to one.
If EVTYPE = 'G' or EVTYPE = 'R', (ER(j) + EI(j)*i)/ED(j),
j = 1,...,N, are the generalized eigenvalues of a pair of
real matrices. If ED(j) is zero, then the j-th generalized
eigenvalue is infinite.
Complex conjugate pairs of eigenvalues must appear
consecutively.
Tolerances
TOLINF DOUBLE PRECISION
If EVTYPE = 'G' or 'R', TOLINF contains the tolerance for
detecting infinite generalized eigenvalues.
0 <= TOLINF < 1.
Error Indicator
INFO INTEGER
= 0: successful exit, i.e., all eigenvalues lie within
the domain of interest defined by DICO, STDOM
and ALPHA;
< 0: if INFO = -i, the i-th argument had an illegal
value;
= 1: some eigenvalues lie outside the domain of interest
defined by DICO, STDOM and ALPHA.
Method
The domain of interest for an eigenvalue lambda is defined by the
parameters ALPHA, DICO and STDOM as follows:
- for a continuous-time system (DICO = 'C'):
Real(lambda) < ALPHA if STDOM = 'S';
Real(lambda) > ALPHA if STDOM = 'U';
- for a discrete-time system (DICO = 'D'):
Abs(lambda) < ALPHA if STDOM = 'S';
Abs(lambda) > ALPHA if STDOM = 'U'.
If EVTYPE = 'R', the same conditions apply for 1/lambda.
Further Comments
NoneExample
Program Text
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