sysdiag

Arguments

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

sysdiag() is obsolete. Please use blockdiag() instead.

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

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.

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).

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

• diag — diagonal including or extracting
• bdiag — block diagonalization, generalized eigenvectors
• repmat — Replicate and tile an array
• brackets — Concatenation. Recipients of an assignment. Results of a function
• feedback — feedback operation

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