A parametric optimization approach to \(H_{\infty}\) and \(H_{2}\) strong stabilization.
This paper presents an approach for designing stable MIMO \(H_\infty\) and \(H_2\) controllers by directly computing the norm-constrained stable transfer matrices \(Q\) in the \(H_\infty\) and \(H_2\) suboptimal controller parametrizations. This is done by first converting the \(H_2\) and \(H_\infty\) strong stabilization problems into some nonlinear unconstrained optimization problems through explicit parametrization 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.
scientific article; zbMATH DE number 1956143