State-Space

Implement linear state-space system

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  • Library:

  • Simulink / Continuous

  • State-Space block

Description

The State-Space block implements a system whose behavior you define as

x˙=Ax+Buy=Cx+Dux|t=t0=x0,

where x is the state vector, u is the input vector, y is the output vector, and x0 is the initial condition of the state vector. The matrix coefficients must have these characteristics:

  • 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.

In general, the block has one input port and one output port. The number of rows in C or D matrix is the same as the width of the output port. The number of columns in the B or D matrix are the same as the width of the input port. If you want to model an autonomous linear system with no inputs, set the B and D matrices to empty. In this case, the block acts as a source block with no input port and one output port, and implements the following system:

x˙=Axy=Cxx|t=t0=x0.

Simulink® software converts a matrix containing zeros to a sparse matrix for efficient multiplication.

Ports

Input

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Real-valued input vector of type double, where the width equals the number of columns in the B and D matrices. For more information, see Description.

Data Types: double

Output

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Real-valued output vector of data type double, with width equal to the number of rows in the C and D matrices. For more information, see Description.

Data Types: double

Parameters

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Specify the matrix coefficient A, as a real-valued n-by-n matrix, where n is the number of states. For more information on the matrix coefficients, see Description.

Programmatic Use

Block Parameter: A
Type: character vector, string
Values: scalar | vector | matrix
Default: '1'

Specify the matrix coefficient B, as a real-valued n-by-m matrix, where n is the number of states and m is the number of inputs. For more information on the matrix coefficients, see Description.

Programmatic Use

Block Parameter: B
Type: character vector, string
Values: scalar | vector | matrix
Default: '1'

Specify the matrix coefficient C as a real-valued r-by-n matrix, where r is the number of outputs and n is the number of states. For more information on the matrix coefficients, see Description.

Programmatic Use

Block Parameter: C
Type: character vector, string
Values: scalar | vector | matrix
Default: '1'

Specify the matrix coefficient D as a real-valued r-by-m matrix, where r is the number of outputs and m is the number of inputs. For more information on the matrix coefficients, see Description.

Programmatic Use

Block Parameter: D
Type: character vector, string
Values: scalar | vector | matrix
Default: '1'

Specify the initial state vector.

Limitations

The initial conditions of this block cannot be inf or NaN.

Programmatic Use

Block Parameter: X0
Type: character vector, string
Values: scalar | vector
Default: '0'

Absolute tolerance for computing block states, specified as a positive, real-valued, scalar or vector. To inherit the absolute tolerance from the Configuration Parameters, specify auto or -1.

  • If you enter a real scalar, then that value overrides the absolute tolerance in the Configuration Parameters dialog box for computing all block states.

  • If you enter a real vector, then the dimension of that vector must match the dimension of the continuous states in the block. These values override the absolute tolerance in the Configuration Parameters dialog box.

  • If you enter auto or –1, then Simulink uses the absolute tolerance value in the Configuration Parameters dialog box (see Solver Pane) to compute block states.

Programmatic Use

Block Parameter: AbsoluteTolerance
Type: character vector, string
Values: 'auto' | '-1' | any positive real-valued scalar or vector
Default: 'auto'

Assign a unique name to each state. If this field is blank (' '), no name assignment occurs.

  • To assign a name to a single state, enter the name between quotes, for example, 'position'.

  • To assign names to multiple states, enter a comma-delimited list surrounded by braces, for example, {'a', 'b', 'c'}. Each name must be unique.

  • To assign state names with a variable in the MATLAB® workspace, enter the variable without quotes. A variable can be a character vector, string, cell array, or structure.

Limitations

  • The state names apply only to the selected block.

  • The number of states must divide evenly among the number of state names.

  • You can specify fewer names than states, but you cannot specify more names than states.

    For example, you can specify two names in a system with four states. The first name applies to the first two states and the second name to the last two states.

Programmatic Use

Block Parameter: ContinuousStateAttributes
Type: character vector, string
Values: ' ' | user-defined
Default: ' '

Model Examples

Double Spring Mass System

Double Spring Mass System

Model a double spring-mass-damper system with a periodically varying forcing function. Associated with the example is an animation function that will automatically open a figure window and display to it. In this system, the only sensor is attached to the mass on the left, and the actuator is attached to the mass on the left. State estimation and LQR control are used.

Open Model
Optical Sensor Image Generation

Optical Sensor Image Generation

Generate a movie with 64 frames and a frame size of 64 by 64 pixels (at 10 frames per second). The movie contains a simulation of a moving target that is moving through a structured background that is itself moving. A jitter motion caused by random vibration is also generated (in a Simulink® model called "aero_vibrati") and the jitter motion is added into the overall sensor motion. Finally, the image is blurred through a Gaussian optical point spread function.

Open Script

Block Characteristics

Data Types

double

Direct Feedthrough

yes

Multidimensional Signals

no

Variable-Size Signals

no

Zero-Crossing Detection

no

Extended Capabilities

See Also

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Topics

Introduced before R2006a

Simulink Documentation

Support