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

The System 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 , , , and with m p. Dd is full rank. The LMI: 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 With the LMI constructed above, the system zeros for a discrete-time LTI system with feedthrough can be found and verified. Implementation The LMI can be implemented using a platform like YALMIP along with an LMI solver such as MOSEK to compute the result. Related LMIs System Zeros without feedthrough System zeros with feedthrough External Links LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes.