LMIs in Control/page/systemzeros with feedthrough

Let's say we have a transfer function defined as a ratio of two polynomials: Zeros are the roots of N(s) (the numerator of the transfer function) obtained by setting and solving for s.The values of the poles and the zeros of a system determine whether the system is stable, and how well the system performs. Similarly, the system zeros are either real or appear in complex conjugate pairs. In the case of system zeros with feedthrough, we take as full rank.


The SystemEdit

Consider a continuous-time LTI system,   , with minimal statespace representation  

 

The DataEdit

The matrices needed as inputs are:

 

In this case,  

The LMI: System Zeros with feedthroughEdit

The transmission zeros of   are the eigenvalues of  . Therefore ,   is a minimum phase if and only if there exists  , where   such that

 

Conclusion:Edit

If P exists, it ensures non-minimum phase. Eigenvalues of   then gives the zeros of the system.

Related LMIsEdit

LMIs_in_Controls/pages/systemzeroswithoutfeedthrough

ImplementationEdit

https://github.com/Ricky-10/coding107/blob/master/systemzeroswithfeedthrough

External LinksEdit

A list of references documenting and validating the LMI.


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