New control method stabilizes delayed systems in real-time

A new paper by Sanguan Zhong and Jie Qi tackles boundary stabilization for first-order hyperbolic partial integro-differential equations (PIDEs) facing both input and state delays at the same time. The authors show this combination complicates control design, especially when the input delay is large and more future state information must be predicted. They develop a backstepping-based boundary controller that achieves stabilization and delay compensation using two affine Volterra transformations with both Fredholm- and Volterra-type integral terms, leading to a system of four PIDE kernel equations. To prove these equations are well-posed, the kernel domain is split along characteristic lines into a finite number of triangular subregions, with the solution built step by step from one subregion to the next. Finite-time stability of the closed-loop system is established, and numerical simulations demonstrate the controller's effectiveness. The paper is 11 pages with 12 figures and was originally submitted to Automatica on October 22, 2025.