A pseudospectra based characterisation of the robust strong Hinfinity norm of timedelay systems with realvalued and structured uncertainties
Abstract
This paper examines the robust (strong) Hinfinity norm of a linear timeinvariant system with discrete delays. The considered system is subject to realvalued, structured, Frobenius norm bounded uncertainties on the coefficient matrices. The robust Hinfinity norm is the worst case value of the Hinfinity norm over the realisations of the system and hence an important measure of robust performance in control engineering. However this robust Hinfinity norm is a fragile measure, as for a particular realization of the uncertainties the Hinfinity norm might be sensitive to arbitrarily small perturbations on the delays. Therefore, we introduce the robust strong Hinfinity norm, inspired by the notion of strong stability of delay differential equations of neutral type, which takes into account both the perturbations on the system matrices and infinitesimal small delay perturbations. This quantity is a continuous function of the nominal system parameters and delays. The main contribution of this work is the introduction of a relation between this robust strong Hinfinity norm and the the pseudospectrum of an associated singular delay eigenvalue problem. This relation is subsequently employed in a novel algorithm for computing the robust strong Hinfinity norm of uncertain timedelay systems. Both the theoretical results and the algorithm are also generalized to systems with uncertainties on the delays, and systems described by a class of delay differential algebraic equations.
 Publication:

arXiv eprints
 Pub Date:
 September 2019
 arXiv:
 arXiv:1909.07778
 Bibcode:
 2019arXiv190907778A
 Keywords:

 Mathematics  Numerical Analysis;
 Electrical Engineering and Systems Science  Systems and Control