Peak-to-Peak Stabilization of Sampled-Data Systems Subject to Actuator Saturation and Its Practical Application to an Inverted Pendulum

• Published in: Mathematics (Basel) Vol. 11; no. 22; p. 4592
• Main Authors: Nguyen, Khanh Hieu, Kim, Sung Hyun
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.11.2023
• Subjects: actuator saturation; Actuators; Closed loops; Control systems; Data systems; Design; Embedded systems; Euclidean space; Innovations; Integrals; inverted pendulum system; Linear matrix inequalities; Mathematical analysis; peak-to-peak performance; Pendulums; Sampled data systems; sampled-data control; Stability criteria; Stabilization; Upper bounds
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math11224592

This paper investigates the local stability and stabilization criteria of sampled-data control systems, taking into account actuator saturation and peak-bounded exogenous disturbances. Specifically, this study introduces two innovations to extend the maximum upper bound of the sampling interval: two novel time integrals of the weighted state derivative are introduced to formulate an improved looped-functional; second, the introduction of two supplementary zero-equalities to improve the relationship among the components of the augmented state. Building on this, a set of linear matrix inequality-based stabilization conditions is derived. These conditions ensure that a closed-loop sampled-data system can become exponentially stable and achieve a guaranteed peak-to-peak performance in the domain of attraction. Finally, the efficacy of the proposed methodology is substantiated through both simulation and experimental results, focusing on the sampled-data control of an inverted pendulum system.