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LMIs in Control/Matrix and LMI Properties and Tools/Discrete Time/Discrete Time Negative Imaginary Lemma
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The System
Given a square, discrete-time LTI system G: L2e --> L2e with state-space realization (Ad, Bd, Cd, Dd) where
, , , and .
In this system, and and .
The Data
, , , and
The LMI:
The system G posed above is considered to be negative imaginary under either of the sufficient and necessary conditions:
There exists , where P > 0 such that
2. There exists , where Q > 0 such that
Conclusion
By using the LMI described above, a discrete LTI system can be evaluated for the negative imaginary condition.
Implementation
This LMI can be implemented in any LMI solver such as YALMIP, using an algorithmic solver like MOSEK.
Related LMIs
Negative Imaginary Lemma
External Links
LMI Properties and Applications in Systems, Stability, and Control Theory - A List of LMIs by Ryan Caverly and James Forbes.