LMIs in Control/Matrix and LMI Properties and Tools/Discrete Time/Discrete Time System Zeros With Feedthrough

The SystemEdit

Given a square, discrete-time LTI system G: L2e --> L2e with minimal state-space realization (Ad, Bd, Cd, Dd) where

 ,  ,  , and   with m   p. Dd is full rank.

The transmission zeros of   are the eigenvalues of:  .

The DataEdit

 ,  ,  , and   with m   p. Dd is full rank.

The LMI:Edit

With the system defined above, it can be seen that G(z) is minimum phase if and only if there exists  , where P > 0, such that:


If the system G is square (m = p), then full rank Dd implies Dd-1 exists and the above LMI simplifies to:



With the LMI constructed above, the system zeros for a discrete-time LTI system with feedthrough can be found and verified.


The LMI can be implemented using a platform like YALMIP along with an LMI solver such as MOSEK to compute the result.

Related LMIsEdit

External LinksEdit