Robust Multi-Objective Feedback Design by Quantifier Elimination

Reviewer: Luminita State

The research reported here addresses the problem of robust multi-objective feedback design in terms of mathematical logic, using new developments in quantifier elimination theory. As is well known, the general static output feedback stabilization problem is lacking an analytical solution, and the high computational complexity of the available software has discouraged interest in the theoretical results that have been obtained so far. The problem of frequency-domain robust multi-objective feedback design and a series of its typical design objectives are presented in the first two sections. Next, all of the performance objectives considered are expressed as quantified polynomial inequalities. Thus, the question of the existence of a solution is reduced to the question of quantifier elimination of the existential quantifier applied to the resulting formula. Several illustrative examples given in the fourth section lead to the conclusions formulated in the final part of the paper. This work can be viewed as an alternative method for robust multi-objective feedback design. As it is supported by the arguments supplied here, the reported technique could work efficiently, at least for some practical problems.