# MTI Toolbox for MATLAB, Version 2.1

The MTI Toolbox for MATLAB provides a suite of tools for working with multilinear time-invariant (MTI) models. Parameters of MTI models can be represented as tensors, i.e., multidimensional or N-way arrays. Tensors offer a wide range of efficient computation and decomposition methods. This toolbox provides many standard methods for modeling, identification, analysis, and controller design of MTI systems.

## Downloading

This toolbox is open source and hosted on mti.systems. See `LICENSE.txt` for the terms of the license (2-clause BSD).

Be advised that a recent version of MATLAB is required. Once you have downloaded or cloned the MTI Toolbox, use `addpath` to add the `mti_toolbox` directory to your path. Type `doc mti_toolbox` to access this documentation. For more information, see `README.md`

## Functionality

The MTI Toolbox provides the classes and functions for manipulating multilinear time-invariant systems using MATLAB's object-oriented features.

- Multilinear Time-Invariant State-Space Models - The MTI Toolbox supports the creation of multilinear time-invariant state-space models. The MTI systems can be initialized in matrix or tensor form.
- Descriptor Multilinear Time-Invariant State-Space Models - The MTI Toolbox supports the creation of descriptor multilinear time-invariant state-space models. The MTI systems can be initialized in matrix or tensor form.

## How to Cite

To support this toolbox and its authors, please cite the appropriate works. The primary references are given below. Additionally, please cite the specific references mentioned in the help or documentation for the functions you are using. Thanks very much for your support.

- General software, latest release: Gerwald Lichtenberg, Enrico Uhlenberg, and others, Multilinear Time-Invariant Toolbox for MATLAB, Version 2.1, mti.systems, October 18, 2025.
- Multilinear Time-Invariant Systems: Lichtenberg, G., Pangalos, G., Cateriano Yáñez, C., Luxa, A., Jöres, N., Schnelle, L. & Kaufmann, C. (2022). Implicit multilinear modeling: An introduction with application to energy systems. at - Automatisierungstechnik, 70(1), 13-30. https://doi.org/10.1515/auto-2021-0133

## More information

This documentation is provided via the MATLAB Help interface under "Supplemental Software" and online at mti.systems.

## Contact

The MTI Toolbox for MATLAB was developed by the Hamburg University of Applied Sciences (HAW Hamburg) in cooperation with the Application Center for Integration of Local Energy Systems (ILES) as part of Fraunhofer IWES and the German Electron Synchrotron (DESY). Please email info@mti.systems with any questions about the toolbox.