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Mixed \(H_ 2/H_ \infty\) control for time-varying and linear parametrically-varying systems. (English) Zbl 0861.93009
The paper provides a solution to the mixed \(H_2/H_\infty\) problem with reduced order controller for time-varying systems in terms of solvability of differential linear matrix inequalities and rank conditions, including a detailed discussion of how to construct a controller. Immediate specializations lead to a solution to the full order problem and to the mixed \(H_2/H_\infty\) problem for linear systems depending on an unknown but, in real-time, measurable time-varying parameter. Under certain conditions on the parameter dependence, the quadratic mixed \(H_2/H_\infty\) problem is completely solved by reducing it to the solution of finitely many algebraic linear matrix inequalities. This includes a new linear matrix inequality solution to the \(h_2\) problem for general linear time-invariant systems, with extended results on the optimal value computation.
Reviewer: S.Curteanu (Iaşi)

93B36 \(H^\infty\)-control
93C99 Model systems in control theory
15A39 Linear inequalities of matrices
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