Stability and Stabilization of Time-delay Systems: An Eigenvalue-based Approach

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Time-delays are important components of many dynamical systems that describe coupling or interconnection between dynamics, propagation, or transport phenomena in shared environments, in heredity, and in competition in population dynamics. This monograph addresses the problem of stability analysis and the stabilisation of dynamical systems subjected to time-delays. It presents a wide and self-contained panorama of analytical methods and computational algorithms using a unified eigenvalue-based approach illustrated by examples and applications in electrical and mechanical engineering, biology, and complex network analysis. This text bridges the fields of control (analysis and feedback design, robustness, and uncertainty) and numerical analysis (explicit algorithms, and methods). The authors provide an overall solution to the (robust) stability analysis and stabilisation problem of linear time-delay systems, which is the result of this cross-fertilisation of control theory, numerical linear algebra, numerical bifurcation analysis and optimisation.