LMIs in Control/Matrix and LMI Properties and Tools/Discrete Time/Discrete Time Negative Imaginary Lemma
The System[edit | edit source]
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[edit | edit source]
, , , and
The LMI:[edit | edit source]
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[edit | edit source]
By using the LMI described above, a discrete LTI system can be evaluated for the negative imaginary condition.
Implementation[edit | edit source]
This LMI can be implemented in any LMI solver such as YALMIP, using an algorithmic solver like MOSEK.
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.