Discrete State-Space

Implements a discrete system in the state space.

blockType: DiscreteStateSpace

Path in the library:

/Basic/Discrete/Discrete State-Space

Description

Block behavior for nonempty matrices

Block Discrete State-Space implements a system described by the following equations:

where

— entrance;
— condition;
— exit.

The coefficients of the matrix should have the following characteristics, as shown in the diagram:

A It must be a matrix of size on , where — the number of states.
B It must be a matrix of size on , where — the number of input parameters.
C It must be a matrix of size on , where — the number of exits.
D It must be a matrix of size on .

discrete state space 1

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

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

Block behavior for empty matrices

When are the matrices A, B and C if they are empty (for example, [;;]), the block functionality becomes:

If the vector Initial conditions If it is also empty, then the block uses the zero vector of the initial state.

Ports

Input

# IN_1 — input signal
scalar | vector | matrix-column

Details

An input vector whose length is equal to the number of columns in the matrices B and D.

Data types	`Float16`, `Float32`, `Float64`, `Int8`, `Int16`, `Int32`, `Int64`, `UInt8`, `UInt16`, `UInt32`, `UInt64`, `Bool`, .
Complex numbers support	No

Output

# OUT_1 — output signal
scalar | vector

Details

Output vector whose length is equal to the number of rows in the matrices C and D.

Data types	`Float64`.
Complex numbers support	No

Parameters

Main

# A — matrix A

Details

matrix coefficient A of size to , where is the number of states.

Default value	`1`
Program usage name	`A`
Tunable	Yes
Evaluatable	Yes

# B — matrix B

Details

matrix coefficient B of size to , where is the number of input parameters.

Default value	`1`
Program usage name	`B`
Tunable	Yes
Evaluatable	Yes

# C — matrix C

Details

matrix coefficient C of size to , where is the number of outputs.

Default value	`1`
Program usage name	`C`
Tunable	Yes
Evaluatable	Yes

# D — matrix D
Scalar / array of real numbers

Details

Matrix coefficient D of size to , where is the number of outputs and is the number of input parameters.

Default value	`1`
Program usage name	`D`
Tunable	Yes
Evaluatable	Yes

# Initial conditions — initial state vector
Scalar / vector of real numbers

Details

Specify the initial state vector.

Default value	`0`
Program usage name	`InitialCondition`
Tunable	Yes
Evaluatable	Yes

# Sample time — interval between calculation steps
SampleTime (real number / vector of two real numbers)

Details

Specify the interval between calculation steps as a non-negative number. To inherit a calculation step, set this parameter to -1.

Default value	`-1`
Program usage name	`SampleTime`
Tunable	No
Evaluatable	Yes

Examples

Example