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

Abstract

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_{\infty} $ 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.

Keywords

• Actuator saturation
• average dwell time
• finite-time boundedness
• L₂-L∞ performance
• Lyapunov-Krasovskii method
• time-varying delay