Please note that the recommended version of Scilab is 2025.0.0. This page might be outdated.
See the recommended documentation of this function
lmisolver
Solve linear matrix inequations.
Calling Sequence
[XLISTF[,OPT]] = lmisolver(XLIST0,evalfunc [,options])
Arguments
- XLIST0
a list of containing initial guess (e.g.
XLIST0=list(X1,X2,..,Xn)
)- evalfunc
a Scilab function ("external" function with specific syntax)
The syntax the function
evalfunc
must be as follows:[LME,LMI,OBJ]=evalfunct(X)
whereX
is a list of matrices,LME, LMI
are lists andOBJ
a real scalar.- XLISTF
a list of matrices (e.g.
XLIST0=list(X1,X2,..,Xn)
)- options
optional parameter. If given,
options
is a real row vector with 5 components[Mbound,abstol,nu,maxiters,reltol]
Description
lmisolver
solves the following problem:
minimize f(X1,X2,...,Xn)
a linear function of
Xi's
under the linear constraints: Gi(X1,X2,...,Xn)=0
for i=1,...,p and LMI (linear matrix inequalities) constraints:
Hj(X1,X2,...,Xn) > 0
for j=1,...,q
The functions f, G, H are coded in the Scilab function
evalfunc
and the set of matrices Xi's in the list X
(i.e. X=list(X1,...,Xn)
).
The function evalfun
must return in the list
LME
the matrices G1(X),...,Gp(X)
(i.e. LME(i)=Gi(X1,...,Xn),
i=1,...,p).
evalfun
must return in the list LMI
the matrices H1(X0),...,Hq(X)
(i.e.
LMI(j)=Hj(X1,...,Xn)
, j=1,...,q).
evalfun
must return in OBJ
the value
of f(X)
(i.e.
OBJ=f(X1,...,Xn)
).
lmisolver
returns in XLISTF
, a
list of real matrices, i. e. XLIST=list(X1,X2,..,Xn)
where the Xi's solve the LMI problem:
Defining Y,Z
and cost
by:
[Y,Z,cost]=evalfunc(XLIST)
, Y
is a list of zero matrices, Y=list(Y1,...,Yp)
,
Y1=0, Y2=0, ..., Yp=0
.
Z
is a list of square symmetric matrices,
Z=list(Z1,...,Zq)
, which are semi positive definite
Z1>0, Z2>0, ..., Zq>0
(i.e.
spec(Z(j))
> 0),
cost
is minimized.
lmisolver
can also solve LMI problems in which
the Xi's
are not matrices but lists of matrices. More
details are given in the documentation of LMITOOL.
Examples
// Find diagonal matrix X (i.e. X=diag(diag(X), p=1) such that //A1'*X+X*A1+Q1 < 0, A2'*X+X*A2+Q2 < 0 (q=2) and trace(X) is maximized // Constants rand("seed", 0); n = 2; A1 = rand(n, n); A2 = rand(n, n); Xs = diag(1:n); Q1 = -(A1'*Xs+Xs*A1+0.1*eye()); Q2 = -(A2'*Xs+Xs*A2+0.2*eye()); function [LME, LMI, OBJ]=evalf(Xlist) X = Xlist(1) LME = X-diag(diag(X)) LMI = list(-(A1'*X+X*A1+Q1), -(A2'*X+X*A2+Q2)) OBJ = -sum(diag(X)) endfunction X = lmisolver(list(zeros(A1)), evalf); // Run optimization, X = [1.0635042 0; 0 2.0784841] X = X(1); [Y, Z, c] = evalf(X) // Check evaluaton function value at the point found // Y = 0 // Z = list([0.0731600 0.7080179; 0.7080179 0.7186999], [0.1154910 0.5345239; 0.5345239 1.4843684]) // c = -1.0635042
See Also
- lmitool — Graphical tool for solving linear matrix inequations.
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