feasp
Compute solution to given system of LMIs
Syntax
Description
[
computes a solution, if any exists, of a system of LMIs and returns a vector
tmin
,xfeas
] = feasp(lmisys
)xfeas
of particular values of the decision variables for which all
LMIs in the system are satisfied.
Given an LMI system,
feasp
computes xfeas
by solving the auxiliary
convex program:
Minimize t subject to NTL(x)N – MTR(x)M ≤ tI.
The global minimum of this program is the scalar value tmin
. The
LMI constraints are feasible if tmin ≤ 0
, and strictly feasible if
tmin < 0
.
Examples
Input Arguments
Output Arguments
Tips
When the least-squares problem solved at each iteration becomes ill conditioned, the
feasp
solver switches from Cholesky-based to QR-based linear algebra (see Memory Problems for details). Since the QR mode typically requires much more memory, MATLAB® may run out of memory and display the following message.??? Error using ==> feaslv Out of memory. Type HELP MEMORY for your options.
If you see this message, increase your swap space. If no additional swap space is available, set
options(4) = 1
. Doing so prevents switching to QR and causesfeasp
to terminate when Cholesky fails due to numerical instabilities.
Algorithms
The feasibility solver of feasp
is based on Nesterov and Nemirovski's
Projective Method described in [1] and [2].
References
[1] Nesterov, Y., and A. Nemirovski, Interior Point Polynomial Methods in Convex Programming: Theory and Applications, SIAM, Philadelphia, 1994.
[2] Nemirovski, A., and P. Gahinet, “The Projective Method for Solving Linear Matrix Inequalities,” Proc. Amer. Contr. Conf., 1994, Baltimore, Maryland, p. 840–844.
Version History
Introduced before R2006a