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Numeric Linear Time-Invariant Models

Common models of linear systems, such as transfer functions and state-space models

Numeric linear-time-invariant (LTI) models are the basic building blocks that you use to represent linear systems. Numeric LTI model objects let you store dynamic systems in commonly-used representations. For example, tf models represent transfer functions in terms of the coefficients of their numerator and denominator polynomials, and ss models represent LTI systems in terms of their state-space matrices. There are also LTI model types specialized for representing PID controllers in terms of their proportional, integral, and derivative coefficients.

Build up a more complex model of a control system by representing individual components as LTI models and connecting the components to model your control architecture. For an example, see Control System Modeling with Model Objects.


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tfTransfer function model
zpkZero-pole-gain model
ssState-space model
frdFrequency-response data model
filtSpecify discrete transfer functions in DSP format
dssCreate descriptor state-space models
pidPID controller in parallel form
pidstdPID controller in standard form
pid22-DOF PID controller in parallel form
pidstd2 2-DOF PID controller in standard form
rssGenerate random continuous test model
drssGenerate random discrete test model


LTI SystemUse linear time invariant system model object in Simulink


Getting Started

Continuous-Time Models

Discrete-Time Models

MIMO Models

LTI Models in Simulink

More About Model Objects

  • Types of Model Objects
    Model object types include numeric models, for representing systems with fixed coefficients, and generalized models for systems with tunable or uncertain coefficients.
  • Dynamic System Models
    Represent systems that have internal dynamics or memory of past states, such as integrators, delays, transfer functions, and state-space models.
  • Numeric Models
    Numeric LTI Models represent dynamic elements, such as transfer functions or state-space models, with fixed coefficients.
  • Static Models
    Represent static input/output relationships, including tunable or uncertain parameters and arrays.