The Wolfram Language provides an extensive suite of built-in functionality to carry out analysis, design, and simulation of continuous- and discrete-time control systems using both classical and modern techniques. Building on the Wolfram Language's proven symbolic architecture, state-space and transfer function models can be represented in symbolic as well as numeric form, yielding closed-form symbolic solutions where traditional tools only provide numerical answers. All built-in numerical solvers use the Wolfram Language's hybrid symbolic-numeric approach and highly efficient numerical algorithms.

Basic Modeling »

TransferFunctionModel — a transfer-function model

StateSpaceModel — a state-space model

ToContinuousTimeModel   ▪ ToDiscreteTimeModel   ▪ ...

Models with Time Delays »

SystemsModelDelay   ▪ TransferFunctionModel   ▪ StateSpaceModel   ▪ ...

Models with Algebraic Constraints »

DescriptorStateSpace   ▪ StateSpaceModel   ▪ ...

Nonlinear Models »

AffineStateSpaceModel   ▪ NonlinearStateSpaceModel   ▪ ...

Model Connections and Manipulations »

SystemsModelSeriesConnect — connects two models in series

SystemsModelExtract — extracts a subsystem

SystemsModelFeedbackConnect   ▪ SystemsModelDelete   ▪ ...

Model Simulations

InputOutputResponse — complete simulation response

InputOutputResponseData — simulation data object

StateResponse   ▪ OutputResponse

Classical Analysis and Design »

RootLocusPlot   ▪ BodePlot   ▪ NyquistPlot   ▪ PIDTune   ▪ ...

Analysis of State-Space Models »

ControllabilityMatrix   ▪ ObservabilityMatrix   ▪ JordanModelDecomposition   ▪ InternallyBalancedDecomposition   ▪ ...

Design using State-Space Models »

StateFeedbackGains   ▪ LQEstimatorGains   ▪ DiscreteLQRegulatorGains   ▪ KalmanEstimator   ▪ ...

Matrix Equation Solvers

RiccatiSolve   ▪ DiscreteRiccatiSolve   ▪ LyapunovSolve   ▪ DiscreteLyapunovSolve

Deploy to Microcontrollers »

MicrocontrollerEmbedCode   ▪ MicrocontrollerCodeData