minreal

Syntax

[AM, BM, CM, DM] = minreal(A, B, C, D)

[AM, BM, CM, DM] = minreal(A, B, C, D, TOL)

SYSM = minreal(SYSIN, TOL)

SYSM = minreal(SYSIN)

Inputs

A

The state matrix (n x n), where n is the number of states.

B

The input matrix (n x p), where p is the number of inputs.

C

The output matrix (q x n), where q is the number of outputs.

D

The direct transmission matrix (q x p).

TOL

The tolerance used for state elimination. Default = sqrt(eps()).

SYSIN

A state-space model.

Outputs

AM

The state matrix (n x n), where n is the number of states.

BM

The input matrix (n x p), where p is the number of inputs.

CM

The output matrix (q x n), where q is the number of outputs.

DM

The direct transmission matrix (q x p).

SYSM

The minimum realization state-space model.

Example

a = [-3.0000   -3.4000;
         0     -3.4000]

b = [1.2000;1.2000]

c = [0.4    -0.4]

d = [1]
    
sys = ss(a, b, c, d)
sysm = minreal(sys)

sys = object [
Scaled: 0
TimeUnit: seconds
ts: 0
a: [Matrix] 2 x 2
-3.00000  -3.40000
 0.00000  -3.40000
b: [Matrix] 2 x 1
1.20000
1.20000
c: [Matrix] 1 x 2
0.40000  -0.40000
d: 1
e: [Matrix] 0 x 0
type: StateSpaceModel
]
sysm = object [
Scaled: 0
TimeUnit: seconds
ts: 0
a: [Matrix] 2 x 2
-4.90000  -1.90000
 1.50000  -1.50000
b: [Matrix] 2 x 1
-1.69706
 0.00000
c: [Matrix] 1 x 2
5.55112e-17  5.65685e-01
d: 1
e: [Matrix] 0 x 0
type: StateSpaceModel
]

Comments

SYSR = The function removes unobservable and/or uncontrollable states in a state-space model.