# Basic 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.

## Functions

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 `tf` Transfer function model `zpk` Zero-pole-gain model `ss` State-space model `frd` Frequency-response data model `filt` Specify discrete transfer functions in DSP format `dss` Create descriptor state-space models
 `pid` PID controller in parallel form `pidstd` PID controller in standard form `pid2` Create 2-DOF PID controller in parallel form, convert to parallel-form 2-DOF PID controller `pidstd2` Create 2-DOF PID controller in standard form, convert to standard-form 2-DOF PID controller
 `rss` Generate random continuous test model `drss` Generate random discrete test model

## Blocks

 LTI System Use linear time invariant system model object in Simulink LPV System Simulate Linear Parameter-Varying (LPV) systems

## Topics

### 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.