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

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.

Mots clés: delay effects; $H_\infty$-stability; fractional systems; Neutral systems

Domaines: Systèmes et contrôle [cs.SY]

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, 2018, 56 (1), pp.538-555. ⟨10.1137/16m1101271⟩. ⟨hal-01679070⟩