On the closest stable descriptor system in the respective spaces \(RH_2\) and \(RH_\infty\). (English) Zbl 1282.15013
Summary: We consider the following approximation problem. Given an unstable linear time-invariant continuous-time descriptor system with transfer function \(G\), find a stable one whose transfer function is the best approximation of \(G\) in the spaces \(RH_2\) and \(RH_\infty\), respectively. Explicit optimal solutions are presented under consideration of numerical issues. An application in the field of stability preserving model reduction is illustrated by some examples.
MSC:
| 15A22 | Matrix pencils |
| 93B11 | System structure simplification |
| 93C05 | Linear systems in control theory |
| 93D99 | Stability of control systems |
Keywords:
model reduction; stability preserving; descriptor system; Nehari problem; Hankel norm approximationSoftware:
benchmodredReferences:
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