A unified approach for the $H_\infty$-stability analysis of classical and fractional neutral systems with commensurate delays

Le Ha Vy Nguyen 1
1 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France, SUPELEC, CNRS - Centre National de la Recherche Scientifique : UMR8506
Abstract : We examine the stability of linear integer-order and fractional-order systems with commensurate delays of neutral type in the sense of $H_\infty$-stability. The systems may have chains of poles approaching the imaginary axis. While several classes of these systems have been previously studied on a case-by-case basis, a unified method is proposed in this paper which allows to deal with all these classes at the same time. Approximation of poles of large modulus is systematically calculated based on a convex hull derived from the coefficients of the system. This convex hull also serves to establish sufficient conditions for instability and necessary and sufficient conditions for stability.
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SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, In press, 56 (1), pp.538-555 〈10.1137/16m1101271 〉
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Le Ha Vy Nguyen. A unified approach for the $H_\infty$-stability analysis of classical and fractional neutral systems with commensurate delays. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, In press, 56 (1), pp.538-555 〈10.1137/16m1101271 〉. 〈hal-01679070〉

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