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.

Functions

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Sparse Models

`sparss`	Sparse first-order state-space model
`mechss`	Sparse second-order state-space model
`getx0`	Map initial conditions from a `mechss` object to a `sparss` object
`full`	Convert sparse models to dense storage
`imp2exp`	Convert implicit linear relationship to explicit input-output relation
`inv`	Invert models
`getDelayModel`	State-space representation of internal delays

Data Access

`sparssdata`	Access first-order sparse state-space model data
`mechssdata`	Access second-order sparse state-space model data
`showStateInfo`	State partition information
`spy (sparss)`	Visualize sparsity pattern of a `sparss` model object
`spy (mechss)`	Visualize sparsity pattern of a `mechss` model object

Time and Frequency Response

`step`	Step response plot of dynamic system; step response data
`impulse`	Impulse response plot of dynamic system; impulse response data
`initial`	Initial condition response of state-space model
`lsim`	Plot simulated time response of dynamic system to arbitrary inputs; simulated response data
`bode`	Bode plot of frequency response, or magnitude and phase data
`nyquist`	Nyquist plot of frequency response
`nichols`	Nichols chart of frequency response
`sigma`	Singular values plot of dynamic system
`passiveplot`	Compute or plot passivity index as function of frequency
`dcgain`	Low-frequency (DC) gain of LTI system
`evalfr`	Evaluate frequency response at given frequency
`freqresp`	Frequency response over grid

Model Interconnection

`interface`	Specify physical connections between components of `mechss` model
`xsort`	Sort states based on state partition
`feedback`	Feedback connection of multiple models
`parallel`	Parallel connection of two models
`append`	Group models by appending their inputs and outputs
`connect`	Block diagram interconnections of dynamic systems
`lft`	Generalized feedback interconnection of two models (Redheffer star product)
`series`	Series connection of two models