tzero

Invariant zeros of linear system.

Syntax

• z = tzero(sys)
• z = tzero(A, B, C, D)
• z = tzero(A, B, C, D, E)
• [z, nrank] = tzero(sys)
• [z, nrank] = tzero(A, B, C, D)
• [z, nrank] = tzero(A, B, C, D, E)

Input argument

• sys - a LTI model.
• A - State matrix: Nx-by-Nx matrix.
• B - Input-to-state matrix: Nx-by-Nu matrix.
• C - State-to-output matrix: Ny-by-Nx matrix.
• D - Feedthrough matrix: Ny-by-Nu matrix.
• E - Nx-by-Nx matrix.

Output argument

• Z - Invariant zeros: column vector.
• nrank - Normal rank: positive integer.

Description

tzero function is employed to extract the invariant zeros of a Multiple Input, Multiple Output (MIMO) dynamic system described by the system model sys.

In cases where sys is a minimal realization, these invariant zeros coincide with the transmission zeros of the system.

Example

A = [1 2; 3 4];
B = [1; 0];
C = [1 0];
D = 0;
sys = ss(A, B, C, D);
z = tzero(sys)
[z, nrank] = tzero(sys)

See also

append.

History

Author

Allan CORNET