MATLAB package StabilityStabilizationPTDS: Stability and Stabilization of Periodic Time-Delay Systems. The software deals with spectrum-based stability assessment and stabilization methods for periodic linear time-delay systems, where the delays and the period of the system matrices are commensurate. The software relies on the dual interpretation of the Floquet multipliers, which can be characterized as non-zero eigenvalues either of the monodromy operor or of a finite-dimensional nonlinear eigenvalue problem, whose solution is obtained by solving an initial value problem. The stability assessment of a periodic time-delay system is determined by the largest in modulus Floquet multiplier. This Floquet multiplier is first approximated by a spectral collocation of the monodromy operator eigenproblem. Hence, its precision is refined up to machine precision by Broyden’s method, considering the finite-dimensional nonlinear eigenvalue problem. The derivate of the Floquet multiplier with respect to system parameter can also be computed. The derivative computation is used in the stabilization method, which designs targeted parameters of the time-delay systems in order to minimize the modulus of the largest Floquet multipliers. The stabilization method requires the usage of the software HANSO (Hybrid Algorithm for Non Smooth Optimization). The package presents additional routines for the stability and stabilization of large-scale periodic time-delay systems. These large-scale routines solve with Arnoldi’s method the discretized aigenvalue problem arising from the monodromy operator. Moreover, they consider a dual time-systems for the Floquet multiplier derivative computation.

References in zbMATH (referenced in 1 article , 1 standard article )

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  1. Michiels, Wim; Fenzi, Luca: Spectrum-based stability analysis and stabilization of time-periodic time-delay systems (2020)