LMIs in Control/Matrix and LMI Properties and Tools/Discrete Time/Discrete Time Negative Imaginary Lemma

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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:

  1. 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]