$\mathcal{H}_2$ Model Reduction for Large-Scale Linear Dynamical Systems
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Abstract
The optimal $\mathcal{H}_2$ model reduction problem is of great importance in the area of dynamical systems and simulation. In the literature, two independent frameworks have evolved focusing either on solution of Lyapunov equations on the one hand or interpolation of transfer functions on the other, without any apparent connection between the two approaches. In this paper, we develop a new unifying framework for the optimal $\mathcal{H}_2$ approximation problem using best approximation properties in the underlying Hilbert space. This new framework leads to a new set of local optimality conditions taking the form of a structured orthogonality condition. We show that the existing Lyapunov- and…
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Topics
Keywords
- Mathematics
- Interpolation (computer graphics)
- Hilbert space
- Reduction (mathematics)
- Applied mathematics
- Orthogonality
- Dynamical systems theory
- Lyapunov function
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