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Mixed \(H_ 2/H_{\infty{}}\) control: A convex optimization approach. (English) Zbl 0748.93031

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.

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
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