Stability Analysis for Time-Varying Systems with Asynchronous Sampling using Contractivity Approach

Frédéric Mazenc (1) , Michael Malisoff (2) , Miroslav Krstic (3)

1 DISCO - Dynamical Interconnected Systems in COmplex Environments
2 LSU - Louisiana State University
3 MAE - UC San Diego - Department of Mechanical and Aerospace Engineering [Univ California San Diego]

We provide new sufficient conditions for a gen- eralized exponential input-to-state stability condition to hold. Our proofs use innovative trajectory based contractivity and cooperative systems arguments. Another key ingredient is a new variant of Halanay’s inequality, which differs from prior Halanay inequalities because of its use of sampling. Our sufficient conditions allow arbitrarily long intervals between some consec- utive sampling times, provided the intervals between consecutive sampling times are frequently small enough. This removes a significant limitation of prior results that relied on versions of Halanay’s inequality that did not contain sampling. Unlike standard stability conditions, the upper bounds for the norm of the current state in our less restrictive exponential input-to-state stability conclusions have suprema of disturbances over intervals that include earlier times than the initial times. We apply our work to a broad class of time-varying continuous time systems with sampling.

Mots clés: Sampling; Linear systems; Stability

Domaines: Automatique

Frédéric Mazenc, Michael Malisoff, Miroslav Krstic. Stability Analysis for Time-Varying Systems with Asynchronous Sampling using Contractivity Approach. IEEE Control Systems Letters, 2021, 5 (1), pp.49-54. ⟨10.1109/lcsys.2020.2999409⟩. ⟨hal-02749259⟩