For 

http://fr.mathworks.com/help/control/ref/tzero.html#bs9l7y9

Dear Elnaz,

The roots of the polynomials Phi(s) on the diagonal of the Smith form of a system matrix, in either state-space or polynomial form, are called the invariant zeros of the system, since these do not change when either constant state or constant output feedback is applied to the system. The function InvariantZeros can be used to determine the invariant zeros of a state-space, transfer-function, system matrix, or left or right matrix-fraction model.

For a systems described by a system matrix P(s), in either states-space form or polynomial form invariant zeros are the roots of the monic greatest common divisor of all maximum order minors of P(s). Where, P(s) also is called system matrix of Rosenbrock.

Here is attached files a detailed explanation of the conceptof invariant zeros.

Best regards

For a given linear system, e.g. in Laplace domain, zeros are the roots of the numerator while the poles are the roots of the denominator. Zeros which are located on the left hand-side are minimum-phase, while on the right-hand side are nonminimum-phase. In a feedback control system, the right-half plane (RHP) zeros cannot be cancelled out by any stable controller law, so these zeros remain at the locations as they are in the open-loop regardless of the controller used. Any attempt to cancel out one of the zero will lead to an unstable controller form and as such suffers from internal instability. On the other hand, if the zeros are on the left-hand plane (LHP), they might be cancelled out or alter by a controller in the closed-loop system - in this case, the controller does not need to have unstable poles; it can cancel the stable zeros using stable poles. Observer often uses known inputs and outputs to estimate the system states, which latter will be used in control. Supposed the system has at least one RHP zero, when there is an inversion calculation involved, the RHP zero will become RHP pole (i.e., unstable pole), which is not desired in any stable observer. Thus, it is important to be assertive that the system zeros are LHP so that any inversion involved will not lead to unstable observer.

Please note that, this explanation is from the layman point of view with minimum mathematical knowledge, But you need a basic feedback control knowledge.