MTI-Toolbox 3.0

Tools for Multilinear Modeling, Simulation, and Analysis.

What the toolbox is

A multilinear time-invariant (MTI) model is linear in each of its variables on its own, but not in all of them at once. That is enough nonlinearity to describe real energy, process and building systems, while keeping a structure that can still be worked with directly. The MTI-Toolbox holds that structure in a tensor, in a decomposed form that avoids the size a full tensor would reach as variables are added, and builds a modelling workflow around it.

With the toolbox you can:

Build a model from matrices, from equation strings, or from symbolic expressions — explicit (mss) or implicit and hybrid (mdss, with algebraic constraints and binary signals).
Simulate it in continuous or discrete time.
Linearize it at an operating point, and convert to and from MATLAB’s standard state-space models with mss.ss2mss, mdss.ss2mdss and mss2mdss.
Identify a model from measured data with mlgreyest, or multilinearize an existing Simulink model with mss.mlinearize.

The project website is mti.systems.

Before you install

The toolbox needs the Optimization Toolbox, and several of its capabilities need further MathWorks products — each licensed separately from MATLAB, and none of which the installer can add for you. One further capability needs a third-party kit, which does ship inside the package. The recommended MATLAB release is R2025a.

See Requirements for the full list, and Installation for the two ways to install the toolbox — the .mltbx installer and the source archive. Run environmentChecker after installing to check your environment against the requirements.

Quick start

Build a first tensor — the .mltbx installer puts the toolbox on your path for you; from the source archive you add src/ yourself:

addpath(genpath('src'));

% Build a CPN tensor from structure/parameter matrices
structureMatrix = [0.5 -0.5; 1 0; 0 1];
parameterMatrix = [2 0; 4 6; 0 8];
obj = CPNTensor(structureMatrix, parameterMatrix);

Overview

The documentation mirrors the src/ folder one to one:

Folder	Contents
`core/`	Abstract base classes (`mtiModel`, `mtiSimulator`, `mtiTensor`)
`model/`	Model classes: multilinear state space (`mss`) and descriptor state space (`mdss`)
`simulator/`	Continuous- and discrete-time simulators for `mss`/`mdss` models
`tensor/`	Tensor representations (`CPNTensor`, `TTTensor`)
`utilities/`	Parsing, symbolic and transformation helpers, plus the environment check

The conversion entry points mss.ss2mss and mdss.ss2mdss are static methods of the model classes: they turn standard state-space models into their multilinear counterparts. mss2mdss is a method of mss and turns an explicit model into a descriptor one.

Where to go next

Requirements — what your MATLAB installation needs.
Installation — the installer and the source archive.
Getting Started — build, simulate and linearize a first model in about twenty lines.
Demos — worked examples you can open and run straight away.
The API reference documents every class and function, starting with the model classes and the tensor representations.

MyToolbox Documentation | Generated automatically by CI/CD pipeline