Optimization of the Smoothed Spectral Abscissa for Retarded Type Systems

Gomez, Marco A.; Michiels, Wim

doi:10.1016/j.ifacol.2019.12.208

Cited by 1 publication

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“…We illustrate the theoretical results applied to the stabilization of a triple integrator with a delay‐based feedback controller in Section 5, and we end the contribution with some final comments in Section 6. A preliminary version of this paper is presented in the work of Gomez and Michiels, where the proofs of Lemma , Theorem , and Theorem are only sketched, and the computation of the derivatives of the delay Lyapunov matrix with respect to the system parameters is carried out in line with the schemes proposed in the work of Gomez et al, which are different from the proposed scheme in Section 4, as previously explained.…”

Section: Introductionmentioning

confidence: 99%

Characterization and optimization of the smoothed spectral abscissa for time‐delay systems

Gomez

Michiels

2019

Intl J Robust & Nonlinear

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Summary We introduce a new robust stability measure for systems with multiple pointwise delays, which is called smoothed spectral abscissa, consistently with the existing measure for delay‐free systems. Its main characteristics are that it is smooth with respect to the system parameters and it provides a trade‐off between the decay rate of the system solution and the scriptH2 norm of a transfer matrix related with the system. The smoothed spectral abscissa is implicitly defined in terms of the scriptH2 norm of an auxiliary system, and its computation is based on the so‐called delay Lyapunov matrix. We show that these features make the smoothed spectral abscissa suitable for the design of robust controllers by using standard gradient‐based optimization techniques and exploiting a novel characterization of the derivatives of the delay Lyapunov matrix with respect to the system parameters.

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Section: Introductionmentioning

confidence: 99%