https://github.com/konimarti/lti

General state-space representation of linear, time-invariant systems in Golang
https://github.com/konimarti/lti

control-systems control-theory golang linear lti lti-system state-space state-space-representation state-space-systems

Last synced: 3 months ago
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General state-space representation of linear, time-invariant systems in Golang

• Host: GitHub
• URL: https://github.com/konimarti/lti
• Owner: konimarti
• License: mit
• Created: 2019-02-06T14:24:29.000Z (about 7 years ago)
• Default Branch: master
• Last Pushed: 2022-03-25T21:12:32.000Z (about 4 years ago)
• Last Synced: 2025-10-07T10:01:12.757Z (7 months ago)
• Topics: control-systems, control-theory, golang, linear, lti, lti-system, state-space, state-space-representation, state-space-systems
• Language: Go
• Homepage:
• Size: 27.3 KB
• Stars: 6
• Watchers: 1
• Forks: 5
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

          
# Linear and time-invariant systems in Golang 

[![License](http://img.shields.io/badge/license-MIT-red.svg?style=flat)](https://github.com/konimarti/lti/blob/master/LICENSE)

[![GoDoc](https://godoc.org/github.com/konimarti/observer?status.svg)](https://godoc.org/github.com/konimarti/lti)

[![goreportcard](https://goreportcard.com/badge/github.com/konimarti/observer)](https://goreportcard.com/report/github.com/konimarti/lti)

```go get github.com/konimarti/lti```

* State-space representation and estimation of linear, time-invariant systems for control theory in Golang

	```math

	 x'(t) = A * x(t) + B * u(t)

	```

	 and

	```math

	 y(t)  = C * x(t) + D * u(t)

	```

* Can be used as an input for a [Kalman filter](http://github.com/konimarti/kalman). 

## Usage

```go

	// define time-continuous linear system

	system, err := lti.NewSystem(

		...

	)

	// check system properties

	fmt.Println("Observable=", system.MustObservable())

	fmt.Println("Controllable=", system.MustControllable())

	// define initial state (x) and control (u) vectors

	...

	// get derivative vector for new state

	fmt.Println(system.Derivative(x, u))

	// get output vector for new state

	fmt.Println(system.Response(x, u))

	// discretize LTI system and propagate state by time step dt

	discrete, err := system.Discretize(dt)

	fmt.Println("x(k+1)=", discrete.Predict(x, u))

}

```

### Example

See example [here](example/lti.go).

## More information

For additional materials on state-space models for control theory, check out the following links:

* A practical guide to state-space control [here](https://github.com/calcmogul/state-space-guide)

* State-space model impelmentation for Arduinos [here](https://github.com/tomstewart89/StateSpaceControl)

## Credits

This software package has been developed for and is in production at [Kalkfabrik Netstal](http://www.kfn.ch/en).