`pole` — Return poles of transfer-function and state-space control models.

pole(sys) returns the roots of the denominator polynomial for a supported SISO tf model, or the eigenvalues of the state matrix for an ss model.

Syntax

p = pole(sys)

Inputs

Name	Type	Required	Default	Description
`sys`	`Any`	Yes	—	SISO tf model.

Returns

Name	Type	Description
`p`	`Any`	Poles of the SISO tf model as a column vector.

Errors

Identifier	When	Message
`RunMat:pole:InvalidModel`	Input system is not a valid SISO tf object.	`pole: invalid model`
`RunMat:pole:UnsupportedModel`	Model form is unsupported.	`pole: unsupported model`
`RunMat:pole:Internal`	Root calculation or output construction failed.	`pole: internal error`

How `pole` works

Supports SISO tf objects.
Supports ss state-space objects by computing eigenvalues of A.
Returns an N x 1 real vector when all poles are real.
Returns an N x 1 complex vector when any pole has a nonzero imaginary part.
Static-gain models return an empty pole vector.

GPU memory and residency

pole returns host-resident vectors.

Example

Second-order poles

H = tf(1, [1 3 2]);
pole(H)

Expected output:

ans = [-1; -2]

How RunMat validates `pole`

pole validates the input model and computes denominator roots or state-matrix eigenvalues through shared control model helpers. Tests cover real, repeated, complex-conjugate, and state-space poles plus VM integration.

Implementation: `crates/runmat-runtime/src/builtins/control/pole.rs`

See Correctness & Trust for the full methodology and coverage table.

Using `pole` with coding agents

Open a RunMat example with live inputs, then ask the agent to explain how pole changes the result.

Run a small pole example, explain the result, then change one input and compare the output.

FAQ

Does pole cancel pole-zero pairs?⌄

No. It returns roots of the stored denominator polynomial for the supplied model.

damp · db · dcgain · feedback · impulse · isstable · nyquist · rlocus · ss · step · stepinfo · tf · zero

Open-source implementation

Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how pole is executed, line by line, in Rust.

View the source for pole in Rust on GitHub
Learn how the RunMat runtime works
Found a bug? Open an issue with a minimal reproduction.

About RunMat

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pole — Return poles of transfer-function and state-space control models.