Stability and Stabilization of Aperiodic Sampled-Data Systems Subject to Control Input Saturation: A Set Invariant Approach

• Published in: IEEE transactions on automatic control Vol. 67; no. 3; pp. 1423 - 1429
• Main Authors: Huff, Daniel Denardi, Fiacchini, Mirko, da Silva, Joao Manoel Gomes
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.03.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE); Institute of Electrical and Electronics Engineers
• Subjects: Asymptotic stability; Automatic; Continuity (mathematics); Control stability; Control systems; Data systems; Engineering Sciences; Input saturation; Liapunov functions; Lyapunov analysis; Nonlinear dynamical systems; Nonlinear dynamics; Power system stability; Sampled data systems; Saturation; Stability analysis; Stability criteria; Time-varying systems; Two dimensional displays; input saturation; sampled-data systems; Lyapunov analysis
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2021.3064988

This article proposes a new method to deal with the stability analysis and stabilization of aperiodic sampled-data control systems subject to input saturation. An impulsive system representation is employed, with a linear flow and a nonlinear jump dynamics, such that the evolution of the system at the sampling instants can be modeled by a difference inclusion defined by two set-valued maps. We show that to ensure the asymptotic stability it is sufficient to verify that a Lyapunov function decreases by a certain amount only at a grid of possible values for the sampling interval, as long as the increase of the function in continuous-time is conveniently bounded. Simulation results compare our approach with other ones.