sos2ss (Signal Processing Toolbox)

Conversion of second-order sections to state-space.

Syntax

[A,B,C,D] = sos2ss(sos)
[A,B,C,D] = sos2ss(sos,g)

Description

sos2ss converts a second-order section representation of a given system to an equivalent state-space representation.

[A,B,C,D] = sos2ss(sos)

converts the system sos, in second-order section form, to a single-input, single-output state-space representation:

The discrete transfer function in second-order section form is given by

sos is a L-by-6 matrix organized as

The entries of sos must be real for proper conversion to state space. The returned matrix A is size N-by-N, where N = 2L-1, B is a length N-1 column vector, C is a length N-1 row vector, and D is a scalar.

[A,B,C,D] = sos2ss(sos,g)

converts the system sos in second-order section form with gain g:

Example

Compute the state-space representation of a simple second-order section system with a gain of 2:

sos = [1  1  1  1  0 -1; -2  3  1  1 10  1];
[A,B,C,D] = sos2ss(sos)
A =
   -10     0    10     1
     1     0     0     0
     0     1     0     0
     0     0     1     0
B =
     1
     0
     0
     0
C =
    21     2   -16    -1
D =
    -2

Algorithm

sos2ss first converts from second-order sections to transfer function using sos2tf, and then from transfer function to state-space using tf2ss.

`sos2tf`	Conversion of second-order sections to transfer function.
`sos2zp`	Conversion of second-order sections to zero-pole-gain.
`ss2sos`	Conversion of state-space to second-order sections.
`tf2ss`	Conversion of transfer function to state-space.
`zp2ss`	Conversion of zero-pole-gain to state-space.