Solution to negative-imaginary control problem for uncertain LTI systems with multi-objective performance

This paper addresses the problem of dynamic output feedback controller synthesis in LMI framework for LTI generalized plants with negative-imaginary uncertainties. The proposed technique transforms the controller synthesized nominal closed-loop system into a strongly strict negative-imaginary system and exploits the DC loop gain condition pertaining to negative-imaginary theory to establish internal stability in presence of negative-imaginary uncertainties. Apart from making the closed-loop system robustly stable, the designed output feedback controller also facilitates multi-objective performance of the closed-loop system such as minimizing the H₂ and H_∞ norms, reducing the peak overshoot, increasing the decay rate, optimizing the settling time, etc. Illustrative examples have been studied to demonstrate the usefulness of the proposed control scheme. A thorough μ-analysis subjected to ‘mixed’ two-block perturbations is included in the examples to show that the designed controller can also facilitate a certain level of robust H_∞ performance in presence of stable NI/SNI uncertainties.