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]- LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes.