Global Exponential Stabilization and Global Lp Performance of a Saturated Double Integrator

• Published in: IEEE control systems letters Vol. 8; pp. 784 - 789
• Main Authors: Martins, Luis, Cardeira, Carlos, Oliveira, Paulo
• Format: Journal Article
• Language: English
• Published: IEEE 2024
• Subjects: Additives; Aerospace electronics; Asymptotic stability; Closed loop systems; Control nonlinearities; Convergence; input saturation; robust stability; stability analysis; Stability criteria; Trajectory
• ISSN: 2475-1456
• DOI: 10.1109/LCSYS.2024.3403471

This letter presents novel results on the simultaneous global internal and external stabilization problem for the double integrator controlled by a saturated static state linear feedback. The methodology capitalizes on the distinctive characteristics of the smooth strictly increasing saturation function considered to strengthen and extend the stability properties reported in the existing literature for this canonical system. Concretely, as the main contributions, this letter demonstrates that the resulting closed-loop system, in the absence of disturbances, is globally exponentially stable and, in the face of non-input additive disturbances, is globally <inline-formula> <tex-math notation="LaTeX">{\mathcal {L}}_{p} </tex-math></inline-formula> stable for any given <inline-formula> <tex-math notation="LaTeX">p \in [1, \infty </tex-math></inline-formula>) and yields a bounded state trajectory. The simulation experiments showcase these new findings.