# LTI System

Use linear time invariant system model object in Simulink

**Libraries:**

Control System Toolbox

## Description

The LTI System block imports linear system model objects into the
Simulink^{®} environment. You specify the LTI model to import in the **LTI
system variable** parameter. You can import any type of proper linear
time-invariant dynamic system model. If the imported system is a state-space (`ss`

) model, you can specify initial state values in the **Initial
states** parameter.

## Examples

### Simulate LTI Model in Simulink

The `LTISystemBlockSimulation`

model shows how to use an LTI System block to simulate the response of a SISO transfer function to a step input.

### Import MIMO LTI Model into Simulink

How to use an LTI System block to represent a MIMO linear system in Simulink®.

## Ports

### Input

**Port_1(In1)** — Input signal

scalar | vector

For a single-input LTI system, the input signal is a scalar. For multiple-input systems, combine the system inputs into a vector signal, using blocks such as:

Mux (Simulink)

Vector Concatenate (Simulink)

Bus Creator (Simulink)

### Output

**Port_1(Out1)** — Output signal

scalar | vector

For a single-output LTI system, the output signal is a scalar. For multiple-output systems, the output signal is a vector. To split system outputs into scalar signals, use blocks such as:

Demux (Simulink)

Bus Selector (Simulink)

## Parameters

**LTI system variable** — Linear system

dynamic system model

Specify the linear system for the block as a MATLAB^{®} expression or a variable in the MATLAB workspace, the model workspace, or a data dictionary. The
model can be SISO or MIMO.

Most linear time-invariant dynamic system models are supported, except:

Frequency-response data models, such as

`frd`

and`genfrd`

models.Nonlinear identified models, such as

`idnlarx`

.Models with unmodeled dynamics, such as

`udyn`

.

The specified model must be proper (see `isproper`

).

The model can be either continuous time or discrete time. When the LTI system block is in a Simulink model with synchronous state control (see the State Control (HDL Coder) block), you must specify a discrete-time model.

Simulink converts the model to its state-space equivalent prior to initializing the simulation.

**Initial states (state-space only)** — Initial state values for state-space model

`[]`

(default) | vector | scalar

If the linear system is in state-space form, specify the initial state
values as a vector with as many entries as the system has states. If you
specify a scalar value, the block applies that value to each state in the
system. The default value, `[]`

, initializes all states to
zero.

The concept of initial state is not well-defined for linear systems that are not in state-space form, such as transfer functions or zero-pole-gain models. For such models, the initial state depends on the choice of state coordinates used by the realization algorithm. As a result, the block ignores this parameter for such models.

**Pade order (for linearization)** — Order of Pade approximation

`0`

(default) | positive integer | vector

Set the order of the Pade approximation for linearization routines.

The default value is

`0`

, which results in a unity gain with no dynamic states.Setting the order to a positive integer

`n`

adds`n`

states to your model, but results in a more accurate linear model of the delay.

Use a vector of positive integers to specify a different order for each input channel.

## Extended Capabilities

### C/C++ Code Generation

Generate C and C++ code using Simulink® Coder™.

## Version History

**Introduced before R2006a**

### R2024a: Simulate state-space models with offsets

You can now simulate a state-space model with offsets using the LTI
System block. Use the **LTI system variable** parameter
to specify a state-space variable containing model offsets in the
`Offsets`

property. Offsets usually arise when linearizing
nonlinear dynamics at some operating conditions. For more information about how to
store offsets, see `ss`

.

### R2024a: Support for LTI models with complex coefficients

You can now simulate LTI models with complex coefficients using the LTI System block.

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