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# zp2ss() - Signal Processing

### Syntax

### Example

### Output / Return Value

### Limitations

### Alternatives / See Also

### Reference

zp2ss converts a zero-pole-gain representation of a given system to an equivalent state-space representation. [A,B,C,D] = zp2ss(z,p,k) finds a single input, multiple output, state-space representationx˙=Ax+Buy=Cx+Dugiven a system in factored transfer function form.H(s)=Z(s)P(s)=k(s−z1)(s−z2)⋯(s−zn)(s−p1)(s−p2)⋯(s−pn)Column vector p specifies the pole locations, and matrix z the zero locations with as many columns as there are outputs. The gains for each numerator transfer function are in vector k. The A, B, C, and D matrices are returned in controller canonical form.Inf values may be used as place holders in z if some columns have fewer zeros than others.

[A,B,C,D] = zp2ss(z,p,k)

State-Space Representation of Mass-Spring SystemOpen This ExampleGenerate the state-space representation of a damped mass-spring system that obeys the differential equation The measurable quantity is the acceleration, , and is the driving force. In Laplace space, the system is represented by The system has unit gain, a double zero at , and two complex-conjugate poles.z = [0 0]; p = roots([1 0.01 1]) k = 1; p = -0.0050 + 1.0000i -0.0050 - 1.0000i Use zp2ss to find the state-space matrices.[A,B,C,D] = zp2ss(z,p,k) A = -0.0100 -1.0000 1.0000 0 B = 1 0 C = -0.0100 -1.0000 D = 1