Stabilisation of neutral systems with saturating control inputs

Abstract

This article focuses on the stabilisation problem of neutral systems in the presence of time-varying delays and control saturation. Based on a descriptor approach and the use of a modified sector relation, global and local stabilisation conditions are derived using Lyapunov–Krasovskii functionals. These conditions, formulated directly as linear matrix inequalities (LMIs), allow one to relate the control law to be computed to a set of admissible initial conditions, for which the asymptotic and exponential stabilities of the closed-loop system are ensured. An extension of these conditions to the particular case of retarded systems is also provided. From the theoretical conditions, optimisation problems with LMI constraints are therefore proposed to compute stabilising state feedback gains with the aim of ensuring stability for a given set of admissible initial conditions or the global stability of the closed-loop system. A numerical example illustrates the application of the proposed results.

Keywords:

• time delay
• saturation
• stabilisation
• stability domains
• robustness

Acknowledgements

J.M. Gomes da Silva Jr is also partially supported by CNPq, Brazil and A. Seuret is partially supported by European Commission through the FeedNetBack project.

Notes

Note

1. A preliminary version of the present work has been presented in Gomes da Silva Jr, Fridman, Seuret, and Richard (2005).