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Invariant zeros of linear system
z = tzero(sys)
z = tzero(A,B,C,D,E)
z = tzero(___,tol)
[z,nrank]
= tzero(___)
z = tzero(sys) returns the invariant zeros of the multi-input, multi-output (MIMO) dynamic system, sys. If sys is a minimal realization, the invariant zeros coincide with the transmission zeros of sys.
z = tzero(A,B,C,D,E) returns the invariant zeros of the state-space model
Omit E for an explicit state-space model (E = I).
z = tzero(___,tol) specifies the relative tolerance, tol, controlling rank decisions.
[z,nrank] = tzero(___) also returns the normal rank of the transfer function of sys or of the transfer function H(s) = D + C(sE – A)^{–1}B.
sys |
MIMO dynamic system model. If sys is not a state-space model, then tzero computes tzero(ss(sys)). |
A,B,C,D,E |
State-space matrices describing the linear system
tzero does not scale the state-space matrices when you use the syntax z = tzero(A,B,C,D,E). Use prescale if you want to scale the matrices before using tzero. Omit E to use E = I. |
tol |
Relative tolerance controlling rank decisions. Increasing tolerance helps detect nonminimal modes and eliminate very large zeros (near infinity). However, increased tolerance might artificially inflate the number of transmission zeros. Default: eps^(3/4) |
z |
Column vector containing the invariant zeros of sys or the state-space model described by A,B,C,D,E. |
nrank |
Normal rank of the transfer function of sys or of the transfer function H(s) = D + C(sE – A)^{–1}B. The normal rank is the rank for values of s other than the transmission zeros. To obtain a meaningful result for nrank, the matrix s*E-A must be regular (invertible for most values of s). In other words, sys or the system described by A,B,C,D,E must have a finite number of poles. |
To calculate the zeros and gain of a single-input, single-output (SISO) system, use zero.
[1] Emami-Naeini, A. and P. Van Dooren, "Computation of Zeros of Linear Multivariable Systems," Automatica, 18 (1982), pp. 415–430.
[2] Misra, P, P. Van Dooren, and A. Varga, "Computation of Structural Invariants of Generalized State-Space Systems," Automatica, 30 (1994), pp. 1921-1936.