madd, msub (Mu Analysis and Synthesis Toolbox)

Mu Analysis and Synthesis Toolbox

madd, msub

Add and subtract CONSTANT, SYSTEM, and VARYING matrices

Syntax

out = madd(mat1,mat2,,matN) 
out = msub(mat1,mat2,,matN)

Description
madd (msub) allows the addition or subtraction of matrices, regardless of their type, as long as their dimensions are compatible. CONSTANT, SYSTEM, and VARYING matrices can be added to or subtracted from one another based on the following table:

mat2
CONSTANT
SYSTEM
VARYING

mat1

CONSTANT

yes
yes
yes

SYSTEM

yes
yes
no

VARYING

yes
no
yes

	`mat2`	CONSTANT	SYSTEM	VARYING
`mat1`
CONSTANT		yes	`yes`	`yes`
SYSTEM		yes	`yes`	`no`
VARYING		yes	`no`	`yes`

For compatibility, the number of rows and columns of mat1 must equal the number of rows and columns of mat2. In the case of SYSTEM matrices, the number of inputs and outputs of mat1 must equal the number of inputs and outputs of mat2. The same is true for VARYING matrices and in addition, the independent variables of the VARYING matrices must be identical. Up to nine matrices of compatible dimension can be added or subtracted by including them as input arguments.

Pictorial Representationof Functions

Examples
Create two SYSTEM matrices p and p1 and a CONSTANT matrix.

a = -10;b = 3;c = 10;d = 0; 
p = pck(a,b,c,d); 
minfo(p)
system:                  1 states 1 outputs1 inputs
a1 = -2; b1 = 3; c1 = 1; d1 = .1; 
p1 = pck(a1,b1,c1,d1); 
minfo(p1)
seesys(p,'3.2g')
-10  |  3
-----|----  
 10  |  0

seesys(p1,'3.2g')
-2  |  3
----|----  
 1  |  .1

Adding two SYSTEM matrices returns a SYSTEM matrix with the same number of inputs and outputs as p and p1.

out = madd(p,p1); 
seesys(out,'3.2g')

-10   0  |   3
0    -2  |   3
---------|------
10    1  |   .1

minfo(out)
system:                      2 states1 outputs1 inputs

Adding a SYSTEM matrix and a CONSTANT matrix returns a SYSTEM matrix with the CONSTANT term added to the D-term of the state-space system.

out = madd(p,a); 
seesys(out,'%3.2g')

-10   |    3
------|-----
 10   |  -10

Subtracting a SYSTEM matrix and a CONSTANT returns a SYSTEM matrix with the CONSTANT term added to the D-term of the state-space system.

out = msub(p,a); 
seesys(out,'%3.2g')

-10   |    3
------|-----
 10   |  -10

Algorithm
madd and msub call the MATLAB + and - commands consistent with the type of matrices.

See Also
+, -, mmult, mscl

indvcmp massign