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# sysdiag

Create a block diagonal matrix from provided inputs or block diagonal system connection

### Syntax

r=sysdiag(a1,a2,...,an)

### Description

Returns the block-diagonal system made with subsystems put in the main diagonal

- ai
subsystems (i.e. gains, or linear systems in state-space or transfer form)

constant, boolean, polynomial or rational matrices of any size

- r
a matrix with a1, a2, a3, ... on the diagonal

### Description

Given the inputs `A`

, `B`

and `C`

,
the output will have these matrices arranged on the diagonal:
.

If all the input matrices are square, the output is known as a block diagonal matrix. |

Used in particular for system interconnections. |

Beside this function, you can also use `sparse()`

primitive to build a *block diagonal sparse matrix*.

For boolean matrices `sysdiag()`

always returns a zero one matrix in the corresponding block
("true" values are replaced by 1 and "false" value by 0).

`sysdiag()`

cannot be used to arrange matrices made of character strings,
but you can overload it (see: overloading).

### Remark

At most 17 arguments.

### Examples

s=poly(0,'s') sysdiag(rand(2,2),1/(s+1),[1/(s-1);1/((s-2)*(s-3))]) sysdiag(tf2ss(1/s),1/(s+1),[1/(s-1);1/((s-2)*(s-3))])

// a matrix of doubles: A=[1 0; 0 1], B=[3 4 5; 6 7 8], C=7 D=sysdiag(A,B,C) // sysdiag([%t %f; %f %t], eye(2,2), ones(3,3)) // a polynomial matrix: s=%s; sysdiag([s 4*s; 4 s^4], [1 s^2 s+2; 3*s 2 s^2-1]) // a rational matrix: sysdiag([1/s 2*s/(4*s+3)], [s; 4; 1/(s^2+2*s+1)]) // a block diagonal sparse matrix: S=sysdiag([1 2; 3 4], [5 6; 7 8], [9 10; 11 12], [13 14; 15 16]) S=sparse(S)

### See also

- brackets — Concatenation. Recipients of an assignment. Results of a function
- insertion — partial variable assignation or modification
- feedback — feedback operation
- diag — diagonal including or extracting
- bdiag — block diagonalization, generalized eigenvectors
- sparse — sparse matrix definition
- repmat — Replicate and tile an array

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