Stabilizing Schrödinger—ODE systems with boundary delay for industrial process optimization

In this paper, we focus on the stabilization of a Schrödinger-ODE cascaded system with boundary delayed control. The system is stabilized through the utilization of integral-type feedback control, in which the integral kernel functions serve as parameters. The objective is to identify an appropriate set of kernel functions that ensure exponential stability characteristics of the closed-loop system. The initial step is to select a target system that must be exponentially stable. We propose an auxiliary system for the task at hand. Initially, we need to establish the equivalence between the auxiliary system and the original controlled time-delay system. This stage is primarily concerned with the elimination of the influence of input memory. The second system is leveraged to ascertain the equivalence between stable target system and the auxiliary system. This paper presents a method to choose parameter functions to create an exponentially stable feedback controller.