PS State-Space

R2026b

Implement linear state-space system

Since R2025a

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PS State-Space block

To add a block to a model, double-click the canvas and start typing the block name. Then, select the block from the list.

Libraries:
Simscape / Foundation Library / Physical Signals / Linear Operators

Description

The PS State-Space block implements a state-space representation of the linear time-invariant system, defined by equations:

$$\begin{array}{l}E\dot{x}=Ax+Bu,\\ y=Cx+Du,\end{array}$$

where:

• x is the dimensionless state vector.

• u is the input vector.

• y is the output vector.

• E is the descriptor matrix.

• A is the state matrix.

• B is the input matrix.

• C is the output matrix.

• D is the feedthrough, or direct transmission matrix.

The state-space model provides a compact and efficient way to represent and analyze systems with multiple inputs and outputs. This model is particularly useful for control design and simulation of dynamic systems.

You can define matrices in your workspace and then use these workspace variables as block parameters.

Examples

Heat Sink Using PS State-Space Block

Use the PS State-Space block to model a heat sink in air. The heat sink represents rods with distributed masses along their lengths. One end of each rod is fixed to a base and undergoes conduction. Heat conducts along the length of each rod. The length of each rod is also exposed to air and undergoes convection with the air.

• Open Model

Ports

Input

U — Input physical signal vector, u, untyped

physical signal

Input physical signal.

Programmatic Use

Port: u

Output

Y — Output physical signal vector, y, untyped

physical signal

Output physical signal.

Programmatic Use

Port: y

Parameters

A — State matrix

[0, 1; -1, -2] (default) | scalar | matrix

State matrix, specified as an n-by-n matrix, where n is the number of states.

Programmatic Use

Parameter: A

B — Input matrix

[0, 1] (default) | scalar | vector | matrix

Input matrix, specified as an n-by-m matrix, where n is the number of states and m is the number of elements in the input vector.

Programmatic Use

Parameter: B

C — Output matrix

[1, 0] (default) | scalar | vector | matrix

Output matrix, specified as an r-by-n matrix, where r is the number of elements in the output vector and n is the number of states.

Programmatic Use

Parameter: C

D — Feedthrough, or direct transmission matrix

0 (default) | scalar | vector | matrix

Feedthrough, or direct transmission matrix, specified as an r-by-m matrix, where r is the number of elements in the output vector and m is the number of elements in the input vector.

Programmatic Use

Parameter: D

E — Descriptor matrix

[1, 0; 0, 1] (default) | scalar | matrix

Mass matrix of the system. The mass matrix can be singular or nonsingular and must have the same dimensions as the state matrix A.

Programmatic Use

Parameter: E

Initial state vector — Initial condition of state vector

[0; 0] (default) | scalar | vector | matrix

Dimensionless vector that represents the initial conditions of the state vector at time t=0.

Programmatic Use

Parameter: x0

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2025a