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

Introduction 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 Consider a square continuous time Linear Time invariant system, with the state space realization The Data The LMI Consider an NI transfer matrix and an NI transfer matrix . The condition λ̅ is satisfied if and only if , Conclusion The above equation holds true if and only if . Implementation This can be implemented in any LMI solver such as YALMIP, using an algorithmic solver like Gurobi. Related LMIs Negative Imaginary Lemma External Links LMI Properties and Applications in Systems, Stability, and Control Theory