%0 Journal Article
%T Generalised Lyapunov functions for discrete-time Lurie systems with slope-restricted nonlinearities
%+ Department of Automatic Control and Systems Engineering [ Sheffield] (ACSE)
%+ Laboratoire des signaux et systèmes (L2S)
%+ CentraleSupélec
%+ Dynamical Interconnected Systems in COmplex Environments (DISCO)
%A Drummond, Ross
%A Valmorbida, Giorgio
%< avec comité de lecture
%@ 0018-9286
%J IEEE Transactions on Automatic Control
%I Institute of Electrical and Electronics Engineers
%8 2023
%D 2023
%R 10.1109/TAC.2022.3233540
%K Lurie systems
%K discrete-time absolute stability
%K Lyapunov functions
%Z Computer Science [cs]/Automatic Control EngineeringJournal articles
%X A class of Lyapunov functions for discrete-time Lurie systems with monotonic non-linearities is proposed. The Lyapunov functions are composed of quadratic terms on the states and of the system's non-linearities as well as Lurie-Postnikov type integral terms. Crucially, positive definiteness of the matrix in the generalised quadratic form and positivity of the scaling terms of the Lurie-Postnikov integrals are relaxed in the stability conditions. Furthermore, they are used for regional stability analysis and performance assessment. Numerical examples show that the proposed Lyapunov function structure matches or outperforms existing ones for these systems.
%G English
%2 https://hal.science/hal-03946093v1/document
%2 https://hal.science/hal-03946093v1/file/DT_Popov%20%282%29.pdf
%L hal-03946093
%U https://hal.science/hal-03946093
%~ CNRS
%~ INRIA
%~ INRIA-SACLAY
%~ SUP_LSS
%~ INRIA_TEST
%~ SUP_SYSTEMES
%~ TESTALAIN1
%~ CENTRALESUPELEC
%~ INRIA2
%~ UNIV-PARIS-SACLAY
%~ UNIVERSITE-PARIS-SACLAY
%~ ANR
%~ GS-COMPUTER-SCIENCE
%~ GS-SPORT-HUMAN-MOVEMENT
%~ DISCO-L2S
%~ INRIA-ROYAUMEUNI