The gain and phase information are the important characteristic quantities of frequency domain for stability analysis and control design.
Many researchers have used LMI as an important tool for stability analysis and control design. Although LMI has a limitation that the feasibility is not guaranteed in some cases, it has been widely used in various control problems because it does not require specific assumptions.
Pak Ji Min, president of Kim Chaek University of Technology, presented a solution to the multivariable version of new Ψ-control and H∞/Ψ-mixed control problems with the phase design criterion that enables solving of some control design problems which cannot be achieved by the H∞-control theory.
First, he derived a new phase condition involving linear matrix inequality (LMI) for multi-input multi-output (MIMO) system. He then proved that the phase condition includes the positive real one for a given system and is guaranteed by the bounded real condition for the corresponding transformed system.
Second, he developed new LMI-based solutions to multivariable Ψ-control for both state feedback and dynamic output feedback. He performed H∞/Ψ-mixed control design by combining H∞-control and Ψ-control.
Finally, he illustrated through design examples the significance of phase criterion in the control design, and the effectiveness of the proposed solutions.
For more information, you can refer to his paper “LMI-Based Solution to Multivariable Ψ-Control and H∞/Ψ-Mixed Control Problems” in “Proceedings of KUTIC-2025”.