Variable Structure Control with Generalized Relays: A Simple Convex Optimization Approach

Laurentiu Hetel (1) , Emilia Fridman (2) , Thierry Floquet (3, 1)

1 LAGIS - Laboratoire d'Automatique, Génie Informatique et Signal
2 Department of Electrical Engineering
3 NON-A - Non-Asymptotic estimation for online systems

The article proposes a convex optimization approach for the design of relay feedback controllers. The case of linear systems is studied in the presence of matched perturbations. The system input is a generalized relay that may take values in a finite set of constant vectors. A simple design method is proposed using Linear Matrix Inequalities (LMIs). Furthermore, the approach is used in the sampled-data case in order to guarantee (locally) the practical stabilization to a bounded ellipsoid of the order of the sampling interval. Time-varying uncertainties (in the state matrix and the sampling interval) can be easily included in the analysis.

Domaines: Automatique / Robotique

Laurentiu Hetel, Emilia Fridman, Thierry Floquet. Variable Structure Control with Generalized Relays: A Simple Convex Optimization Approach. IEEE Transactions on Automatic Control, 2015, 60 (2), pp.497 - 502. ⟨10.1109/TAC.2014.2331417⟩. ⟨hal-01006389⟩