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

Abstract

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.