arXiv subjects

Tudor C. Ionescu

Publications and source records attributed to Tudor C. Ionescu.

5 recordsLinked to original sources

arXiv2026

Moment Matching for Descriptor Systems: A Möbius Mapping Approach

For a class of single-input single-output systems described by proper or improper transfer functions, we propose moment-matching procedures applicable in both continuous- and discrete-time contexts. The resulting technique is not only more flexible and reliable than other procedures which are currently available in literature, but it also enables the placement of constraints on the reduced-order model's poles and zeros. This constraint-based feature, hitherto available only for continuous-time state-space systems, is illustrated via a numerical example based on a practical problem from literature.

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arXiv2026

Time-Domain Moment Matching for Second-Order Systems [Extended Version]

The paper develops a second-order time-domain moment matching framework for the structure-preserving model reduction of high-dimensional second-order dynamical systems, avoiding the first-order double-sized equivalent representation. The moments of a second-order system are characterized by the solutions of second-order Sylvester equations, leading to families of parameterized second-order reduced models that match the moments of the original system at selected interpolation points. A two-sided moment matching problem is also addressed, yielding a unique second-order reduced system that matches two distinct sets of interpolation points. Furthermore, we construct reduced second-order systems that match the moments of both the transfer function and its first-order derivative. Then, we also discuss how the proposed framework can be extended to multiple-input multiple-output (MIMO) second-order systems through tangential interpolation, and we identify the main open difficulties in extending the derivative-matching and pole-zero placement results to the MIMO setting. The theory is illustrated on a numerical example of vibrating systems.

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arXiv2024

Moment matching based reduced closed-loop design to achieve asymptotic performance

In this paper, the moment matching techniques are adopted to obtain reduced-order closed-loop systems with reduced-order controllers that maintain the closed-loop stability and guarantee desired asymptotic performance, after revealing the relationship between the Internal Model Principle used in control design and the time-domain moment matching problem. As a result, the design of a low order controller can be done starting from considering the achieving of asymptotic performance as a moment matching problem, resulting in a reduced order closed-loop system.

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arXiv2021

Model reduction with pole-zero placement and high order moment matching

In this paper, we compute a low order approximation of a system of large order $n$ that matches $ν$ moments of order $j_i$ of the transfer function, at $ν$ interpolation points, has $\ell$ poles and $k$ zeros fixed and also matches $ν-(\ell +k)$ moments of order $j_i+1$, where $j_i+1$ is the multiplicity of the $i$-th interpolation point. We derive explicit linear systems in the free parameters to simultaneously achieve the required pole-zero placement and match the desired high order moments. We compute the closed form of the free parameters that meet the constraints, as the solution of a $ν$ order linear system. Furthermore, for data-driven model reduction, we generalize the construction of the Loewner matrices to include the data and the imposed pole and higher order moment constraints. The resulting approximations achieve a trade-off between the good norm approximation and the preservation of the dynamics of the original system in a region of interest.

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arXiv2013

Families of moment matching based, structure preserving approximations for linear port Hamiltonian systems

In this paper we propose a solution to the problem of moment matching with preservation of the port Hamiltonian structure, in the framework of time-domain moment matching. We characterize several families of parameterized port Hamiltonian models that match the moments of a given port Hamiltonian system, at a set of finite interpolation points. We also discuss the problem of Markov parameters matching for linear systems as a moment matching problem for descriptor representations associated to the given system, at zero interpolation points. Solving this problem yields families of parameterized reduced order models that achieve Markov parameter matching. Finally, we apply these results to the port Hamiltonian case, resulting in families of parameterized reduced order port Hamiltonian approximations.

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