Khargonekar, Pramod P.; Rotea, Mario A. Mixed \(H_ 2/H_{\infty{}}\) control: A convex optimization approach. (English) Zbl 0748.93031 IEEE Trans. Autom. Control 36, No. 7, 824-837 (1991). The paper considers a problem of mixed \(H_ 2/H_ \infty\)-control within the area of multivariable robust control theory. The presented method is suitable for design of a linear, time-invariant controller that stabilizes a linear, time-invariant plant while respecting prescribed performance and robustness constraints. More specifically, the state- feedback problem is first considered so as to keep a mixed \(H_ 2/H_ \infty\) performance criterion below a prescribed value \(\alpha\) and a matrix norm (related to robustness properties) below an other prescribed threshold \(\gamma\). It is shown that the state-feedback controller with constant gain may lead arbitrarily close to the minimal \(H_ 2/H_ \infty\) performance measure. Moreover, the state-feedback problem can be converted into a convex optimization problem over a bounded subset of real matrices but no numerical algorithm for its solution is suggested or demonstrated. Finally, it is shown that the output feedback problem can be reduced to a state-feedback problem. Reviewer: M.Papageorgiou (München) Cited in 124 Documents MSC: 93B51 Design techniques (robust design, computer-aided design, etc.) 93B36 \(H^\infty\)-control 93C40 Adaptive control/observation systems 93B52 Feedback control 93C15 Control/observation systems governed by ordinary differential equations 93C35 Multivariable systems, multidimensional control systems Keywords:multivariable robust control theory; robustness; state-feedback problem PDFBibTeX XMLCite \textit{P. P. Khargonekar} and \textit{M. A. Rotea}, IEEE Trans. Autom. Control 36, No. 7, 824--837 (1991; Zbl 0748.93031) Full Text: DOI