LMIs in Control/Matrix and LMI Properties and Tools/Negative Imaginary System DC Constraint
Introduction edit
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 System edit
Consider a square continuous time Linear Time invariant system, with the state space realization
The Data edit
The LMI edit
Consider an NI transfer matrix and an NI transfer matrix . The condition λ̅ is satisfied if and only if
- ,
- ,
Conclusion edit
The above equation holds true if and only if .
Implementation edit
This can be implemented in any LMI solver such as YALMIP, using an algorithmic solver like Gurobi.