Information about variables and term content of LMIs
lmiinfo provides qualitative
information about the system of LMIs
includes the type and structure of the matrix variables, the number
of diagonal blocks in the inner factors, and the term content of each
lmiinfo is an interactive facility where
the user seeks specific pieces of information. General LMIs are displayed
N' * L(x) * N < M' * R(x) * M
N,M denote the outer factors and
left and right inner factors. If the outer factors are missing, the
LMI is simply written as
L(x) < R(x)
If its right side is zero, it is displayed as
N' * L(x) * N < 0
Information on the block structure and term content of
also available. The term content of a block is symbolically displayed
C1 + A1*X2*B1 + B1'*X2*A1' + a2*X1 + x3*Q1
with the following conventions:
X1, X2, x3 denote the problem variables.
X indicates matrix variables while lower-case
scalar variables. The labels 1,2,3 refer to the first, second, and
third matrix variable in the order of declaration.
Cj refers to constant terms. Special
I and –
Aj, Bj denote the left and right
coefficients of variable terms. Lower-case letters such as
a scalar coefficient.
Qj is used exclusively with scalar
variables as in
Aj, Bj, Cj, Qj is
a dummy label. Hence
C1 may appear in several blocks
or several LMIs without implying any connection between the corresponding
constant terms. Exceptions to this rule are the notations
+ B1'*X2'*A1' which indicate symmetric terms and symmetric
pairs in diagonal blocks.
Consider the LMI
where the matrix variables are X of Type
1, Y of Type 2, and z scalar.
If this LMI is described in
lmis, information about X and
the LMI block structure can be obtained as follows:
lmiinfo(lmis) LMI ORACLE ------- This is a system of 1 LMI with 3 variable matrices Do you want information on (v) matrix variables (l) LMIs (q) quit ?> v Which variable matrix (enter its index k between 1 and 3) ? 1 X1 is a 2x2 symmetric block diagonal matrix its (1,1)-block is a full block of size 2 ------- This is a system of 1 LMI with 3 variable matrices Do you want information on (v) matrix variables (l) LMIs (q) quit ?> l Which LMI (enter its number k between 1 and 1) ? 1 This LMI is of the form 0 < R(x) where the inner factor(s) has 2 diagonal block(s) Do you want info on the right inner factor ? (w) whole factor (b) only one block (o) other LMI (t) back to top level ?> w Info about the right inner factor block (1,1) : I + a1*X1 + A2*X2*B2 + B2'*X2'*A2' block (2,1) : A3*X1 block (2,2) : x3*A4 (w) whole factor (b) only one block (o) other LMI (t) back to top level ------- This is a system of 1 LMI with 3 variable matrices Do you want information on (v) matrix variables (l) LMIs (q) quit ?> q It has been a pleasure serving you!
Note that the prompt symbol is ?> and that answers are either
indices or letters. All blocks can be displayed at once with option
or you can prompt for specific blocks with option
lmiinfo does not provide access to the numerical
value of LMI coefficients.