# Sparse State-Space Models

Efficiently represent, combine and analyze large scale state-space models with sparse data in MATLAB^{®} and Simulink^{®}. Using sparse representation is ideal and efficient since dense model representations for large-scale models are computationally expensive and may lead to very long execution times. For more information, see Computational Advantages of Sparse Matrices.

With the available functionality, you can:

Perform time-domain and frequency-domain response analysis using sparse models

Specify signal-based connections between sparse models and with other LTI models

Specify physical couplings between sparse model components

Transform sparse models between continuous-time and discrete-time representations

Linearize to a sparse model when your Simulink model has a Descriptor State-Space (Simulink) or Sparse Second Order block using

`linearize`

(Simulink Control Design) functionLinearize a structural or a thermal PDE model to a sparse model using

`linearize`

(Partial Differential Equation Toolbox) function

For more details about sparse models and the available functionality, see Sparse Model Basics.

## Functions

## Blocks

Descriptor State-Space | Model linear implicit systems |

Sparse Second Order | Represent sparse second-order models in Simulink (Since R2020b) |

## Topics

**Sparse Model Basics**Sparse models represent state-space systems composed of large sparse matrices.

**Rigid Assembly of Model Components**Specify rigid physical couplings in a structural model.

**Thermal Modeling and Control Design for CPU Chip Cooling System**

Create a CPU and heat sink thermal model, perform model order reduction, and design a controller for a cooling system.