`isstable` — Test stability of SISO transfer-function models.

isstable(sys) returns true when all continuous-time poles are in the open left-half plane, or all discrete-time poles are inside the unit circle.

Syntax

tf = isstable(sys)

Inputs

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

Returns

Name	Type	Description
`tf`	`LogicalArray`	True when all continuous poles are in the open left-half plane or all discrete poles are inside the unit circle.

Errors

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

How `isstable` works

Supports SISO tf objects.
Continuous-time stability requires real(pole) < 0.
Discrete-time stability requires abs(pole) < 1.
Static-gain models are stable.

GPU memory and residency

isstable returns a host logical scalar.

Example

Stable first-order model

H = tf(1, [1 1]);
isstable(H)

Expected output:

ans = logical
   1

How RunMat validates `isstable`

isstable validates the input model, computes poles, and applies continuous or discrete stability rules. Tests cover stable continuous-time models and VM integration.

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

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

Using `isstable` with coding agents

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

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

FAQ

Does marginal stability return true?⌄

No. Poles on the imaginary axis or unit circle are not considered stable by this predicate.

db · dcgain · feedback · impulse · nyquist · pole · ss · step · stepinfo · tf

Open-source implementation

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

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

About RunMat

RunMat is an open-source runtime that executes MATLAB-syntax code blazing on any GPU. It is licensed under the Apache 2.0 license.

RunMat automatically optimizes your math for GPU execution on Apple, Nvidia, and AMD hardware. No code changes needed. Simulations that took hours now take minutes.
Start running code in seconds. RunMat runs in the browser, on the desktop, or from the CLI. No license server, no IT ticket.

Getting started · Benchmarks · Pricing

isstable — Test stability of SISO transfer-function models.