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

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The System[edit | edit source]

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 Data[edit | edit source]

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

The LMI:[edit | edit source]

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:


Conclusion[edit | edit source]

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

Implementation[edit | edit source]

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

Related LMIs[edit | edit source]

External Links[edit | edit source]