balreal (Control Design and Simulation Module, MathScript Function)
Member of the ssanals class.
Syntax
SysBalSS = balreal(SysIn)
[SysBalSS, d] = balreal(SysIn)
[SysBalSS, d, T] = balreal(SysIn)
[SysBalSS, d, T, Tinv] = balreal(SysIn)
Description
Balances a state-space model. A balanced state-space model has identical controllability and observability diagonal Grammians. This function also returns the transformation matrix this function uses to balance the model.
Inputs
Name | Description |
SysIn | Specifies a linear time-invariant (LTI) system in transfer function, zero-pole-gain, or state-space form. |
Outputs
Name | Description |
SysBalSS | Returns the balanced LTI state-space model that results when this function applies the transformation matrix T to the SysIn model. |
d | Returns the diagonal vector of the observability and controllability Grammians of the SysBalSS model. d is a real vector. |
T | Returns the transformation matrix this function uses to balance the SysIn model. This function calculates the T matrix using the Cholesky decomposition of the controllability and observability Grammians of the SysIn model. T is a real matrix. |
Tinv | Returns the inverse of the transformation matrix T. Tinv is a real matrix. |
Examples
SysIn = ss([-1, 0; 0.1, -3], [1, 0]', [0, 1], 0)[SysBalSS, d, T, Tinv] = balreal(SysIn)