**Purpose**

To check stability/antistability of finite eigenvalues with respect to a given stability domain.

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(*)

**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.

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.

TOLINF DOUBLE PRECISION If EVTYPE = 'G' or 'R', TOLINF contains the tolerance for detecting infinite generalized eigenvalues. 0 <= TOLINF < 1.

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.

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.

None

**Program Text**

None

None

None