ss2ss

State coordinate transformation for state-space model

Syntax

sysT = ss2ss(sys,T)

Description

Given a state-space model sys with equations

x˙=Ax+Buy=Cx+Du

or the innovations form used by the identified state-space (IDSS) models:

dxdt=Ax+Bu+Key=Cx+Du+e

(or their discrete-time counterpart), ss2ss performs the similarity transformation x¯=Tx on the state vector x and produces the equivalent state-space model sysT with equations.

x¯˙=TAT1x¯+TBuy=CT1x¯+Du

or, in the case of an IDSS model:

x¯˙=TAT1x¯+TBu+TKey=CT1x¯+Du+e

sysT = ss2ss(sys,T) returns the transformed state-space model sysT given sys and the state coordinate transformation T. The model sys must be in state-space form and the matrix T must be invertible. ss2ss is applicable to both continuous- and discrete-time models.

Examples

Perform a similarity transform to improve the conditioning of the A matrix.

T = balance(sys.a)
sysb = ss2ss(sys,inv(T))

See Also

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