ss2zp (Signal Processing Toolbox)

Conversion of state-space to zero-pole-gain.

Syntax

[z,p,k] = ss2zp(A,B,C,D,iu)

Description

ss2zp converts a state-space representation of a given system to an equivalent zero-pole-gain representation. The zeros, poles, and gains of state-space systems represent the transfer function in factored form.

[z,p,k] = ss2zp(A,B,C,D,iu)

calculates the transfer function in factored form

of the system

from the iu-th input. Returned column vector p contains the pole locations of the denominator coefficients of the transfer function. Matrix z contains the numerator zeros in its columns, with as many columns as there are outputs y. Column vector k contains the gains for each numerator transfer function.

ss2zp also works with systems in discrete time, in which case it returns the z-transform representation. The input state-space system must be real.

The ss2zp function is part of the standard MATLAB language.

Example

Here are two ways of finding the zeros, poles, and gains of a system:

b = [2 3]; 
a = [1 0.4 1];
[z,p,k] = tf2zp(b,a)
z =
    -1.5000
p =
    -0.2000 + 0.9798i
    -0.2000 - 0.9798i
k =
    2
[A,B,C,D] = tf2ss(b,a);
[z,p,k] = ss2zp(A,B,C,D,1)
z =
    -1.5000
p =
    -0.2000 + 0.9798i
    -0.2000 - 0.9798i
k =
    2

Algorithm

ss2zp finds the poles from the eigenvalues of the A array. The zeros are the finite solutions to a generalized eigenvalue problem:

z = eig([A B;C D], diag([ones(1,n) 0]);

In many situations this algorithm produces spurious large, but finite, zeros. ss2zp interprets these large zeros as infinite.

ss2zp finds the gains by solving for the first nonzero Markov parameters.

See Also


`pzmap`	Pole-zero map of LTI system (Control System Toolbox User's Guide).
`sos2zp`	Conversion of second-order sections to zero-pole-gain.
`ss2sos`	Conversion of state-space to second-order sections.
`ss2tf`	Conversion of state-space to transfer function.
`tf2zp`	Conversion of transfer function to zero-pole-gain.
`zp2ss`	Conversion of zero-pole-gain to state-space.

References

[1] Laub, A.J., and B.C. Moore. "Calculation of Transmission Zeros Using QZ Techniques." Automatica 14 (1978). Pg. 557.

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