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

The SystemEdit

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 DataEdit

 ,  ,  , and  

The LMI:Edit

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




By using the LMI described above, a discrete LTI system can be evaluated for the negative imaginary condition.


This LMI can be implemented in any LMI solver such as YALMIP, using an algorithmic solver like MOSEK.

Related LMIsEdit

External LinksEdit