Dissipativity-Preserving Model Reduction for Large-Scale Distributed Control Systems


We have a tendency to propose a dissipativity-preserving structured model reduction method for distributed control systems. As a elementary tool to develop structured model reduction, we have a tendency to first establish dissipativity-preserving model reduction for general linear systems on the premise of a singular perturbation approximation. To the present end, by deriving a tractable expression of singular perturbation models, we characterize dissipativity preservation in terms of a projection-like transformation of storage functions, and we show that the resultant approximation error is relevant to the add of neglected eigenvalues of an index matrix. Next, utilizing this dissipativity-preserving model reduction, we develop a structured controller reduction method for distributed control systems. The major significance of this technique is to preserve the spatial distribution of dissipative controllers and to produce an a priori sure for the performance degradation of closed-loop systems in terms of the $cal H_2 $-norm. The efficiency of the proposed methodology is verified through a numerical example of vibration suppression management for interconnected second-order systems.

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