A parametric optimization approach to H∞ and H2 strong stabilization

This paper presents an approach for designing stable MIMO H"~ and H"2 controllers by directly computing the norm-constrained stable transfer matrices Q in the H"~ and H"2 suboptimal controller parameterizations. This is done by first converting the H"2 and H"~ strong stabilization problems into some nonlinear unconstrained optimization problems through explicit parameterization of the norm-constrained Q's for any fixed order. Then, a two-stage numerical search is carried out by using a combination of a genetic algorithm and a quasi-Newton algorithm in order to reach an optimal solution. The effectiveness of the proposed algorithms is illustrated through some benchmark numerical examples.

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