ctrbf (Control Design and Simulation Module, MathScript Function)
Member of the ssanals class.
Syntax
[As, Bs, Cs, T, l] = ctrbf(SysInSS)
[As, Bs, Cs, T, l] = ctrbf(SysInSS, tol)
[As, Bs, Cs, T, l] = ctrbf(A, B, C)
[As, Bs, Cs, T, l] = ctrbf(A, B, C, tol)
Description
Calculates the controllable staircase representation of the SysInSS system model. This function also returns a list of controllable states.
Inputs
| Name | Description |
| SysInSS | Specifies a linear time-invariant (LTI) model in state-space form. |
| 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. |
| tol | Specifies the tolerance. If a diagonal value in the A matrix is less than the value of tol, this function considers that value equal to 0. The default value of tol is 0.0001. tol is a real scalar. |
Outputs
| Name | Description |
| As | Returns the controllability staircase state matrix A. The controllable states are in the lower right corner of the matrix. As is a real matrix. |
| Bs | Returns the controllability staircase input matrix B. The controllable inputs are in the lower right corner of the matrix. Bs is a real matrix. |
| Cs | Returns the controllability staircase output matrix C. The controllable outputs are in the lower right corner of the matrix. Cs is a real matrix. |
| T | Returns the controllability transformation matrix. T is a real matrix. |
| l | Returns the indexes of the controllable states of the SysInSS model. l is an integer vector. |
Examples
A = [-1, 2; 0, -3]B = [0; 1]
C = [1, 0]
[As, Bs, Cs] = ctrbf(A, B, C)