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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 using linearize (Simulink Control Design) function

  • Linearize 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.


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sparssSparse first-order state-space model (Since R2020b)
mechssSparse second-order state-space model (Since R2020b)
getx0Map initial conditions from a mechss object to a sparss object (Since R2020b)
fullConvert sparse models to dense storage (Since R2020b)
imp2expConvert implicit linear relationship to explicit input-output relation
invInvert dynamic system models
getDelayModelState-space representation of internal delays
findopCompute operating condition from specifications (Since R2023b)
fixInput Fix value of some inputs and delete them (Since R2024a)
sparssdataAccess first-order sparse state-space model data (Since R2020b)
mechssdataAccess second-order sparse state-space model data (Since R2020b)
showStateInfoState vector map for sparse model (Since R2020b)
spyVisualize sparsity pattern of a sparse model (Since R2020b)
stepStep response of dynamic system
impulseImpulse response plot of dynamic system; impulse response data
initialSystem response to initial states 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 value plot of dynamic system
passiveplotCompute or plot passivity index as function of frequency
dcgainLow-frequency (DC) gain of LTI system
evalfrEvaluate system response at specific frequency
freqrespEvaluate system response over a grid of frequencies
interfaceSpecify physical connections between components of mechss model (Since R2020b)
xsortSort states based on state partition (Since R2020b)
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
linearizeLinear approximation of Simulink model or subsystem
linearizeOptionsSet linearization options
linioCreate linear analysis point for Simulink model, Linear Analysis Plots block, or Model Verification block
linearizeLinearize structural or thermal model (Since R2021b)
linearizeInputSpecify inputs to linearized model (Since R2021b)
linearizeOutputSpecify outputs of linearized model (Since R2021b)


Descriptor State-SpaceModel linear implicit systems
Sparse Second OrderRepresent sparse second-order models in Simulink (Since R2020b)