Total stability of equilibria motivates integral action in discrete-time nonlinear systems

Samuele Zoboli (1) , Daniele Astolfi (1) , Vincent Andrieu (1)

1 LAGEPP - Laboratoire d'automatique, de génie des procédés et de génie pharmaceutique

Robustness guarantees are important properties to be looked for during control design. They ensure stability of closedloop systems in face of uncertainties, unmodeled effects and bounded disturbances. Inspired by the continuous-time literature, in this article we investigate the total stability properties of dynamical discrete-time nonlinear systems. Such a property locally relates phase plots of dynamical systems of the same dimension which are "similar enough". As a consequence, it enables the analysis of robustness properties via simple model difference in the discrete-time context. First, we study how existence of equilibria for a nominal model transfers to sufficiently similar ones. Then, we provide results on the propagation of stability guarantees to perturbed systems. Finally, we relate such properties to the constant output regulation problem by motivating the use of discrete-time integral action in discrete-time nonlinear systems for model robustness purposes.

Domaines: Systèmes et contrôle [cs.SY]

Samuele Zoboli, Daniele Astolfi, Vincent Andrieu. Total stability of equilibria motivates integral action in discrete-time nonlinear systems. Automatica, 2023, 155, pp.111154. ⟨10.1016/j.automatica.2023.111154⟩. ⟨hal-04179625v2⟩