LMIs in Control/Click here to continue/LMIs in system and stability Theory/Discrete-time Negative Imaginary Lemma
Appearance
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.