Enhancing Stability and Robust <i>H</i>∞ Control in Consumer Electronics Through Discrete Impulsive Switched Systems

Every consumer electronic device incorporates a power supply circuit to furnish energy, inevitably exposing it to external interference. Consequently, it becomes paramount to mitigate such external interference, which disrupts system operation, while still achieving the necessary system performance. This study investigates challenges associated with achieving exponential stability and robust <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> control in a broad range of discrete switched systems affected by impulsive signals. Different from conventional stability analyses applied to switched hybrid systems, this study undertakes a comprehensive integration of impulses into the formulation of the Lyapunov functional. To address these issues, we propose the utilization of a time-varying impulse-dependent Lyapunov functional to comprehensively capture the dynamic characteristics inherent in discrete-time switched systems. This innovative approach allows us to establish a novel stability criterion, thereby ensuring the feasibility of addressing the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> control problem. Additionally, we propose an effective computational approach for designing switched feedback controllers, relying on inverse matrix calculation techniques, facilitated by the use of convex combinations. Finally, we illustrate the application of the derived <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> control findings to discrete impulsive hybrid systems by presenting a switched RLC circuit model, and give a simulation comparison with the common methods to display the validity of the proposed control scheme.