Dynamic practical stabilization of sampled-data linear distributed parameter systems

Ying Tan (1) , Emmanuel Trélat (2) , Yacine Chitour (3) , Dragan Nesic (1)

1 Department of Electrical and Electronic Engineering [Melbourne]
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
3 LM-Orsay - Laboratoire de Mathématiques d'Orsay

In this paper, dynamic practical stability properties of infinite-dimensional sampled-data systems are discussed. A family of finite-dimensional discrete-time controllers are first designed to uniformly exponentially stabilize numerical approximate models that are obtained from space and time discretization. Sufficient conditions are provided to ensure that these controllers can be used to drive trajectories of infinite-dimensional sampled-data systems to a neighborhood of the origin by properly tuning the sampling period, space and time discretization parameters and choosing an appropriate filtering process for initial conditions.

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Ying Tan, Emmanuel Trélat, Yacine Chitour, Dragan Nesic. Dynamic practical stabilization of sampled-data linear distributed parameter systems. 2009. ⟨hal-00366232v1⟩