# Discrete State-Space

Implement discrete state-space system

Discrete

## Description

### Block Behavior for Non-Empty Matrices

The Discrete State-Space block implements the system described by

$\begin{array}{c}x\left(n+1\right)=Ax\left(n\right)+Bu\left(n\right)\\ y\left(n\right)=Cx\left(n\right)+Du\left(n\right),\end{array}$

where u is the input, x is the state, and y is the output. The matrix coefficients must have these characteristics, as illustrated in the following diagram:

• A must be an n-by-n matrix, where n is the number of states.

• B must be an n-by-m matrix, where m is the number of inputs.

• C must be an r-by-n matrix, where r is the number of outputs.

• D must be an r-by-m matrix.

The block accepts one input and generates one output. The width of the input vector is the number of columns in the B and D matrices. The width of the output vector is the number of rows in the C and D matrices. To define the initial state vector, use the Initial conditions parameter.

To specify a vector or matrix of zeros for A, B, C, D, or Initial conditions, use the `zeros` function.

### Block Behavior for Empty Matrices

When the matrices A, B, and C are empty (for example, `[]`), the functionality of the block becomes `y(n) = Du(n)`. If the Initial conditions vector is also empty, the block uses an initial state vector of zeros.

## Data Type Support

The Discrete State Space block accepts and outputs a real signal of type `single` or `double`. For more information, see Data Types Supported by Simulink in the Simulink® documentation.

## Parameters and Dialog Box

A, B, C, D

Specify the matrix coefficients, as defined in the Description section.

Initial conditions

Specify the initial state vector. The default value is `0`. Simulink does not allow the initial states of this block to be `inf` or `NaN`.

Sample time (–1 for inherited)

Specify the time interval between samples. See Specify Sample Time.

State name

Use this parameter to assign a unique name to the block state. The default is `' '`. When this field is blank, no name is assigned. When using this parameter, remember these considerations:

• A valid identifier starts with an alphabetic or underscore character, followed by alphanumeric or underscore characters.

• The state name applies only to the selected block.

This parameter enables State name must resolve to Simulink signal object when you click Apply.

State name must resolve to Simulink signal object

Select this check box to require that the state name resolve to a Simulink signal object. This check box is cleared by default.

State name enables this parameter.

Selecting this check box disables Code generation storage class.

Package

Select a package that defines the custom storage class you want to apply. If you have defined any packages of your own, click Refresh. This action adds all user-defined packages on your search path to the package list.

Code generation storage class

Select custom storage class for state.

Default: `Auto`

`Auto`

Auto is the appropriate storage class for states that you do not need to interface to external code.

`SimulinkGlobal`

`model_P` initializes the state to its corresponding value in the workspace.

`ExportedGlobal`

State is stored in a global variable

`ImportedExtern`

`model_private.h` declares the state as an extern variable.

`ImportedExternPointer`

`model_private.h` declares the state as an extern pointer.

`Default`

A non-editable placeholder storage class is created.

`BitField`

A `struct` declaration is created that embeds Boolean data.

`Volatile`

Volatile type qualifier is used in state declaration.

`ExportToFile`

Header `(.h)` file containing global variable declarations is generated with user-specified name.

`ImportFromFile`

Predefined header `(.h)` files containing global variable declarations are included.

`FileScope`

A static qualifier is generated in front of the state declaration to make the state visible only to the current file.

`Struct`

A `struct` declaration is created to encapsulate parameter or signal object data.

`StructVolatile`

Volatile type qualifier is used in `struct` declaration.

`GetSet`

Supports specialized function calls to read and write memory.

State name enables this parameter.

The list of valid storage classes differs based on the Package selection.

Setting this parameter to `ExportedGlobal`, `ImportedExtern`, or `ImportedExternPointer` enables Code generation storage type qualifier.

Code generation storage type qualifier

Specify a Simulink Coder storage type qualifier. The default is `' '`. When this field is blank, no qualifier is assigned.

The Simulink Coder product does not check this string for errors. Thus, whatever value you enter appears automatically in the variable declaration.

Setting Code generation storage class to `ExportedGlobal`, `ImportedExtern`, or `ImportedExternPointer` enables this parameter.

During simulation, the block uses the following values:

• The initial value of the signal object to which the state name is resolved

• Min and Max values of the signal object

## Characteristics

 Data Types Double | Single Sample Time Specified in the Sample time parameter Direct Feedthrough Only if D ≠ 0 Multidimensional Signals No Variable-Size Signals No Zero-Crossing Detection No Code Generation Yes