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Balancing based model reduction for structured index-2 unstable descriptor systems with application to flow control. (English) Zbl 1330.93084

Summary: Stabilizing a flow around an unstable equilibrium is a typical problem in flow control. Model-based designed of modern controllers like LQR/LQG or \(H_\infty\) compensators is often limited by the large-scale of the discretized flow models. Therefore, model reduction is usually needed before designing such a controller. Here we suggest an approach based on applying balanced truncation for unstable systems to the linearized flow equations usually used for compensator design. For this purpose, we modify the ADI iteration for Lyapunov equations to deal with the index-2 structure of the underlying descriptor system efficiently in an implicit way. The resulting algorithm is tested for model reduction and control design of a linearized Navier-Stokes system describing von Kármán vortex shedding.

MSC:

93B40 Computational methods in systems theory (MSC2010)
93B11 System structure simplification
93B18 Linearizations
65F30 Other matrix algorithms (MSC2010)
65F50 Computational methods for sparse matrices
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