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Sparse State-Space Models

Large scale state-space models with sparse data

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

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


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sparssSparse first-order state-space model
mechssSparse second-order state-space model
getx0Map initial conditions from a mechss object to a sparss object
fullConvert sparse models to dense storage
imp2expConvert implicit linear relationship to explicit input-output relation
invInvert models
getDelayModelState-space representation of internal delays
sparssdataAccess first-order sparse state-space model data
mechssdataAccess second-order sparse state-space model data
showStateInfoState partition information
spy (sparss)Visualize sparsity pattern of a sparss model object
spy (mechss)Visualize sparsity pattern of a mechss model object
stepStep response plot of dynamic system; step response data
impulseImpulse response plot of dynamic system; impulse response data
initialInitial condition response of state-space model
lsimPlot simulated time response of dynamic system to arbitrary inputs; simulated response data
bodeBode plot of frequency response, or magnitude and phase data
nyquistNyquist plot of frequency response
nicholsNichols chart of frequency response
sigmaSingular values plot of dynamic system
passiveplotCompute or plot passivity index as function of frequency
dcgainLow-frequency (DC) gain of LTI system
evalfrEvaluate frequency response at given frequency
freqrespFrequency response over grid
interfaceSpecify physical connections between components of mechss model
xsortSort states based on state partition
feedbackFeedback connection of multiple models
parallelParallel connection of two models
appendGroup models by appending their inputs and outputs
connectBlock diagram interconnections of dynamic systems
lftGeneralized feedback interconnection of two models (Redheffer star product)
seriesSeries connection of two models


Descriptor State-SpaceModel linear implicit systems
Sparse Second OrderRepresent sparse second-order models in Simulink


Sparse Model Basics

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

Featured Examples