ISS Inequalities for Vector Versions of Halanay's Inequality and of the Trajectory-Based Approach

Frederic Mazenc (1, 2) , Michael Malisoff (3)

1 DISCO - Dynamical Interconnected Systems in COmplex Environments
2 L2S - Laboratoire des signaux et systèmes
3 LSU - Louisiana State University

Halanay's inequality is a powerful and widely used tool to prove asymptotic convergence properties of functions that arise in the study of systems with delays or continuousdiscrete features. In its standard form, it applies to scalar valued functions that satisfy decay conditions, with overshoots depending on suprema of the functions over suitable intervals. Then it provides an exponential decay estimate on the scalar functions. Here, we provide vector versions of Halanay's inequality, and of the so-called trajectory based approach, both yielding input-to-state stability (or ISS) inequalities. Our proofs of the inequalities use the theory of positive systems. We apply our results to prove ISS for interval observers and other cases.

Mots clés: Stability; delay; positive systems; Halanay's inequality

Domaines: Automatique

Frederic Mazenc, Michael Malisoff. ISS Inequalities for Vector Versions of Halanay's Inequality and of the Trajectory-Based Approach. European Journal of Control, 2022, ⟨10.1016/j.ejcon.2022.100665⟩. ⟨hal-03711662⟩