Journal article
Finite-gain Lp stability for hybrid dynamical systems
D Nešić, AR Teel, G Valmorbida, L Zaccarian
Automatica | Published : 2013
Abstract
We characterize the finite-gain Lp stability properties for hybrid dynamical systems. By defining a suitable concept of the hybrid L p norm, we introduce hybrid storage functions and provide sufficient Lyapunov conditions for the Lp stability of hybrid systems, which cover the well-known continuoustime and discrete-time Lp stability notions as special cases. We then focus on homogeneous hybrid systems and prove a result stating the equivalence among local asymptotic stability of the origin, global exponential stability, existence of a homogeneous Lyapunov function with suitable properties for the hybrid system with no inputs, and input-to-state stability, and we show how these properties all..
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Awarded by National Science Foundation
Funding Acknowledgements
This research was supported in part by AFOSR grant FA9550-09-1-0203 and NSF grants ECCS-0925637 and CNS-0720842. The first author is supported by the Australian Research Council under the Discovery Project and Future Fellowship schemes. The third author is supported by Grant EP/J010537/1. The fourth author is supported in part by ENEA-Euratom and by HYCON2 Network of Excellence "Highly-Complex and Networked Control Systems", grant agreement 257462. The material in this paper was partially presented at the 4th IFAC Conference on Analysis and Design of Hybrid Systems (ADHS 12), June 6-8, 2012, Eindhoven, The Netherlands. This paper was recommended for publication in revised form by Associate Editor Andrea Serrani under the direction of Editor Miroslav Krstic.