Computation of Robust Controllers using Symbolic-Numeric Methods

This paper proposes a new heuristic to synthesize m - 1 order H ∞ -controllers for m -order SISO linear systems. Combining a reformulation of the standard H ∞ -synthesis problem in terms of real solutions of a multivariate polynomial system with modern symbolic-numeric methods, such as the Rational Univariate Representation and numerical root isolation, we show how to compute a m - 1 order H ∞ -controller and the suboptimal robust radius for low-order systems. Finally, we compare the proposed algorithm with McFarlane’s algorithm on a few standard examples.