On stability of sets for sampled-data nonlinear inclusions via their approximate discrete-time models and summability criteria

Dragan Nesic (1) , Antonio Loria (2) , Elena Panteley (2) , Andrew Teel (3)

1 Department of Electrical and Electronic Engineering [Melbourne]
2 L2S - Laboratoire des signaux et systèmes
3 CCDC - Center for Control, Dynamical-Systems, and Computation [Santa Barbara]

This paper consists of two main parts. In the first part, we provide a framework for stabilization of arbitrary (not necessarily compact) closed sets for sampled-data nonlinear differential inclusions via their approximate discrete-time models. We generalize [19, Theorem 1] in several different directions: we consider stabilization of arbitrary closed sets, plants described as sampleddata differential inclusions and arbitrary dynamic controllers in the form of difference inclusions. Our result does not require the knowledge of a Lyapunov function for the approximate model, which is a standing assumption in [21] and [19, Theorem 2]. We present checkable conditions that one can use to conclude semi-global asymptotic (SPA) stability, or global exponential stability (GES), of the sampled-data system via appropriate properties of its approximate discrete-time model.

Mots clés: difference inclusions; Sampled-data systems; stability

Domaines: Systèmes dynamiques [math.DS]

Dragan Nesic, Antonio Loria, Elena Panteley, Andrew Teel. On stability of sets for sampled-data nonlinear inclusions via their approximate discrete-time models and summability criteria. SIAM Journal on Control and Optimization, 2009, 48 (3), pp.1888−1913. ⟨hal-00447620⟩