ss2ss

State coordinate transformation for state-space model

Syntax

sysT = ss2ss(sys,T)

Description

Given a state-space model sys with equations

$\begin{array}{l} \dot{x} = A x + B u \\ y = C x + D u \end{array}$

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

$\begin{matrix} \frac{d x}{d t} = A x + B u + K e \\ y = C x + D u + e \end{matrix}$

(or their discrete-time counterpart), ss2ss performs the similarity transformation $\bar{x} = T x$ on the state vector x and produces the equivalent state-space model sysT with equations.

$\begin{array}{l} \dot{\bar{x}} = T A T^{- 1} \bar{x} + T B u \\ y = C T^{- 1} \bar{x} + D u \end{array}$

or, in the case of an IDSS model:

$\begin{array}{l} \dot{\bar{x}} = T A T^{-}^{1} \bar{x} + T B u + T K e \\ y = C T^{-}^{1} \bar{x} + D u + e \end{array}$

(IDSS models require System Identification Toolbox™ software.)

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))

Documentation

ss2ss

Syntax

Description

Examples

See Also

Control System Toolbox Documentation

Support