Jarlebring, Elias; Damm, Tobias; Michiels, Wim Model reduction of time-delay systems using position balancing and delay Lyapunov equations. (English) Zbl 1272.93036 Math. Control Signals Syst. 25, No. 2, 147-166 (2013). Summary: Balanced truncation is a standard and very natural approach to approximate dynamical systems. We present a version of balanced truncation for model order reduction of linear time-delay systems. The procedure is based on a coordinate transformation of the position and preserves the delay structure of the system. We therefore call it (structure-preserving) position balancing. To every position, we associate quantities representing energies for the controllability and observability of the position. We show that these energies can be expressed explicitly in terms of the solutions to corresponding delay Lyapunov equations. Apart from characterizing the energies, we show that one block of the (operator) controllability and observability Gramians in the operator formulation of the time-delay system can also be characterized with the delay Lyapunov equation. The delay Lyapunov equation undergoes a contragredient transformation when we apply the position coordinate transformation and we propose to truncate it in a classical fashion, such that positions which are only weakly connected to the input and the output in the sense of the energy concepts are removed. Cited in 21 Documents MSC: 93B11 System structure simplification 93B17 Transformations 93C15 Control/observation systems governed by ordinary differential equations Keywords:time-delay systems; model reduction; balanced truncation; Lyapunov equations Software:Algorithm 432 × Cite Format Result Cite Review PDF Full Text: DOI Link References: [1] Antoulas A (2005) Approximation dynamical systems. In: Society for industrial and applied mathematics (SIAM). 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