Descriptor state-space models can include both dynamic and algebraic equations, as is common in electrical circuits or constrained mechanical systems. This makes modeling easier and allows for more general systems. Wolfram Language descriptor state-space models generalize the full suite of modeling, analysis, and design functionality supported by standard state-space models.

Modeling & Simulation

StateSpaceModel — model a linear descriptor system

TransferFunctionModel — model an improper transfer function

ToDiscreteTimeModel   ▪ StateSpaceTransform   ▪ ...

SystemsModelSeriesConnect   ▪ SystemsModelFeedbackConnect   ▪ ...

OutputResponse   ▪ StateResponse   ▪ ...

Controller & Estimator Design

StateFeedbackGains — pole placement-based feedback gains

LQEstimatorGains — LQ-based state estimator gains

LQRegulatorGains   ▪ KalmanEstimator   ▪ ...

Analysis & Transformations

KroneckerModelDecomposition — decouple fast and slow subsystems

ControllabilityMatrix   ▪ ObservabilityGramian   ▪ ...