Local Stabilization for Multiple Input-Delay Systems Subject to Saturating Actuators: The Continuous-Time Case

• Published in: IEEE transactions on automatic control Vol. 67; no. 6; pp. 3090 - 3097
• Main Authors: Chen, Yonggang, Wang, Zidong, Shen, Bo, Han, Qing-Long
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.06.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Actuators; Continuous-time systems; Control systems; Control theory; Deduction; Delay effects; Delays; Initial conditions; Linear matrix inequalities; local stabilization; Mathematical analysis; multiple input delays; Optimization; saturating actuators; Stabilization; Symmetric matrices
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2021.3092556

In this article, the local stabilization problem is dealt with for a class of continuous-time multiple input-delay systems subject to saturating actuators. Using the generalized sector conditions and the piecewise Lyapunov-Krasovskii functional, and carrying out rigorous mathematical deduction, a sufficient condition is established under which the closed-loop dynamics is exponentially stable for admissible initial conditions. Subsequently, the explicit characterization of controller gains is obtained in terms of the solvability of linear matrix inequalities. The special cases concerning the constant and single delays are also discussed. Moreover, optimization problems are proposed to maximize the estimate of the domain of attraction. Finally, two examples are given to show the effectiveness and advantages of the obtained results.