Conference Proceedings

Explicit Lyapunov functions for stability and performance characterizations of FOREs connected to an integrator

Luca Zaccarian, Dragan Nesic, Andrew R Teel

Proceedings of the 45th IEEE Conference on Decision and Control | IEEE | Published : 2006


In this paper we provide explicit Lyapunov functions that prove that a First Order Reset Element (FORE) in negative feedback interconnection with an integrator is exponentially stable for any, positive or negative, value of the pole of the FORE. The Lyapunov functions also allow to establish finite gain L2 stability from a disturbance input acting at the input of the plant to the plant output. L2 stability is established by giving a bound on the corresponding L2 gains. The framework used for the characterization of the system dynamics and for the stability and performance analysis corresponds to the ideas first proposed in (Nesic et al. IFAC 2005) and (Zaccarian et al. ACC 2005).


Awarded by ARC Australian Professorial Fellowship and Discovery

Awarded by ARO

Awarded by NSF

Awarded by AFOSR

Funding Acknowledgements

Work supported in part by ARC under the Australian Professorial Fellowship and Discovery Grant DP DP0451177, ARO under Grant no. DAAD19-03-1-0144, NSF under Grants no. CCR-0311084 and ECS-0324679, AFOSR under Grant no. FA9550-06-1-0134, ENEA-Euratom and MIUR under PRIN and FIRB projects.