Finite-Time Boundedness of Switched Time-Varying Delay Systems with Actuator Saturation: Applications in Water Pollution Control

• Published in: IEEE access Vol. 12; p. 1
• Main Authors: Shanmugam, Saravanan, Ali, M. Syed, Narayanan, G., Rhaima, Mohamed
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01.01.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">L <sub xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">2 -<italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">L <sub xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">∞ performance; Actuator saturation; Actuators; Average dwell time; Behavioral sciences; Control systems; Delay; Dwell time; Finite-time boundedness; Linear matrix inequalities; Lyapunov-Krasovskii method; L₂-L∞ performance; Mathematical analysis; Pollution control; Switched systems; Switches; Symmetric matrices; Time-varying delay; Water pollution
• ISSN: 2169-3536; 2169-3536
• DOI: 10.1109/ACCESS.2023.3347613

This paper addresses the challenge of ensuring finite-time boundedness in switched time-varying delay systems with actuator saturation. Utilizing Lyapunov-Krasovskii functionals, we establish delay-dependent conditions through linear matrix inequalities, ensuring that switched systems with time-varying delays remain finite-time bounded. The paper also introduces the concept of average dwell time for switching signals, providing additional conditions for finite-time boundedness. Furthermore, the finite-time L 2 - L ∞ performance of switched systems with time-varying delays is investigated as a measure of disturbance capability within a finite-time interval. The estimator gain matrix can be determined by solving the linear matrix inequalities. The effectiveness of the proposed approach is illustrated through numerical examples.