POLES

The poles of a linear time-invariant system are the roots of the denominator polynomial of its transfer function.

If the denominator is written as

a_n s^n + a_{n-1} s^{n-1} + \cdots + a_1 s + a_0 = 0

then the poles are the complex values of s that satisfy this equation. Pole locations determine whether the system is stable, oscillatory, slow, or fast. This wrapper returns the real and imaginary parts of the poles as a 2-row array.

Excel Usage

=POLES(sysdata)

• sysdata (list[list], required): System data (numerator, denominator rows).

Returns (list[list]): A 2-row array: [Real, Imaginary].

Example 1: System poles

Inputs:

sysdata
1
1

Excel formula:

=POLES({1;1,2,1})

Expected output:

Result
-1	-1
0	0

Python Code

Show Code

import control as ct
import numpy as np

def poles(sysdata):
    """
    Compute the poles of a linear system.

    See: https://python-control.readthedocs.io/en/latest/generated/control.poles.html

    This example function is provided as-is without any representation of accuracy.

    Args:
        sysdata (list[list]): System data (numerator, denominator rows).

    Returns:
        list[list]: A 2-row array: [Real, Imaginary].
    """
    try:
        def flatten(x):
            if x is None: return None
            if not isinstance(x, list): return [float(x)]
            res = []
            for row in x:
                if isinstance(row, list):
                    for v in row:
                        if v is not None and str(v).strip() != "":
                            res.append(float(v))
                elif row is not None and str(row).strip() != "":
                    res.append(float(row))
            return res if res else None

        if not sysdata or len(sysdata) < 2:
            return "Error: sysdata must contain numerator and denominator rows"
        num = flatten(sysdata[0])
        den = flatten(sysdata[1])
        if not num or not den:
            return "Error: Invalid numerator or denominator arrays"
        sys = ct.tf(num, den)
        p = ct.poles(sys)
        if len(p) == 0:
            return [[""], [""]]
        return [
            [float(value) for value in np.real(p)],
            [float(value) for value in np.imag(p)],
        ]
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

sysdata *

System data (numerator, denominator rows).