canon (Control Design and Simulation Module, MathScript Function)

Member of the ssanals class.

Syntax

SysCanSS = canon(SysInSS)

SysCanSS = canon(SysInSS, formtype)

SysCanSS = canon(A, B, C, D)

SysCanSS = canon(A, B, C, D, formtype)

[SysCanSS, T] = canon(SysInSS)

[SysCanSS, T] = canon(SysInSS, formtype)

[SysCanSS, T] = canon(A, B, C, D)

[SysCanSS, T] = canon(A, B, C, D, formtype)

Description

Transforms a state-space system model to a canonical form using the formtype that you specify. This function also returns the transformation matrix that this function uses to transform the model.

Examples

Inputs

Name	Description
SysInSS	Specifies a linear time-invariant (LTI) system in transfer function, zero-pole-gain, or state-space form. This function converts transfer function and zero-pole-gain models to state-space form before transforming the model into canonical form.
formtype	Specifies the canonical form this function uses to transform the SysIn model into the SysCanSS model. method is a string that can take the following values: 'modal' (Default) A is a bi-diagonal matrix. The elements in the main diagonal are the real part of the eigenvalues of A, while elements in the upper secondary or lower secondary diagonal represent the imaginary part of the eigenvalues of A. Therefore, A is strictly diagonal if and only if all eigenvalues are real. 'companion' A has the coefficients of the characteristic polynomial of A in its top row.
A	Specifies an n x n state matrix, where n is the number of states. The default is an empty matrix. A is a real matrix.
B	Specifies an n x m input matrix, where m is the number of inputs. The default is an empty matrix. B is a real matrix.
C	Specifies an r x n output matrix, where r is the number of outputs. The default is an empty matrix. C is a real matrix.
D	Specifies an r x m direct transmission matrix. The default is an empty matrix. D is a real matrix.

Outputs

Name	Description
SysCanSS	Returns an LTI model in state-space form that is the canonical realization of SysInSS.
T	Returns the transformation matrix this function uses to transform the SysInSS model into the SysCanSS model. T is a real matrix.

Examples

SysInSS = ss([1, 1; -1, 2], [1, 2]', [2, 1], 0)
[SysCanSS, T] = canon(SysInSS, 'modal')

Related Topics

ctrb
ctrbf
ss
ss2ss