LMIs in Control/Matrix and LMI Properties and Tools/Negative Imaginary System DC Constraint

IntroductionEdit

These systems are often related to systems involving energy dissipation. But the standard Positive real theory will not be helpful in establishing closed-loop stability. However, transfer functions of systems with a degree more than one can be satisfied with the negative imaginary conditions for all frequency values and such systems are called systems with negative imaginary frequency response.

The SystemEdit

Consider a square continuous time Linear Time invariant system, with the state space realization  

 

The DataEdit

 

The LMIEdit

Consider an NI transfer matrix   and an NI transfer matrix  . The condition λ̅   is satisfied if and only if

 ,

ConclusionEdit

The above equation holds true if and only if  .

ImplementationEdit

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

Related LMIsEdit

External LinksEdit