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\(H_\infty\) model reduction for port-controlled Hamiltonian systems. (English) Zbl 1351.93051

Summary: This paper is concerned with the problem of \(H_\infty\) model reduction for the linear port-controlled Hamiltonian systems. The development includes both the continuous- and discrete-time cases. Some sufficient conditions are obtained for the existence of solutions in terms of linear matrix inequalities (LMIs) and a coupling non-convex rank constraint set. In addition, an explicit parametrization of the desired reduced-order model can be constructed if these conditions are satisfied. Furthermore, the conditions based on the strict LMIs without rank constraint are derived for the zeroth-order \(H_\infty\) approximation problem. Finally, the effectiveness of the proposed model reduction method is illustrated via a practical example.

MSC:

93B36 \(H^\infty\)-control
93B11 System structure simplification
70Q05 Control of mechanical systems
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