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\(\mathcal H_\infty\) and \(\mathcal L_2/\mathcal L_\infty\) model reduction for system input with sector nonlinearities. (English) Zbl 1062.93020

Summary: This paper investigates the problems of model reduction for linear continuous-time systems with input sector nonlinearities. Two objectives (\(\mathcal H_\infty\) and \(\mathcal L_2/\mathcal L_\infty\)) are employed to evaluate the approximation performance and the problems are solved by using linear matrix inequality (LMI) techniques, with sufficient conditions obtained for the existence of desired reduced-order models. Since some matrix inequality constraints are involved in these conditions, the cone complementarity linearization idea is utilized to cast the nonconvex feasibility problem into a sequential minimization problem subject to LMI constraints. A numerical example is presented to show the effectiveness of the proposed theories.

MSC:

93B36 \(H^\infty\)-control
93B11 System structure simplification
15A39 Linear inequalities of matrices
65F10 Iterative numerical methods for linear systems
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