Truncated predictor feedback for a chain of infinite-delayed systems with input saturation

A linear system can be regulated by a control signal through a cascade of integrators, as extensively documented in existing literature. However, such controllers often encounter challenges when each link in this chain is affected by time delays, leading to poor performance or even instability. This paper addresses a particularly challenging scenario wherein each connection experiences infinite delays, and the input signal is subject to saturation. To overcome these issues, we propose a truncated predictor feedback controller via the low-gain design. Semi-global stabilization problem of the considered system is solved with the peak magnitude of the input signal provided. One of the novelties of our work lies in the expanded applicability of truncated predictor feedback, which is applied to a system featuring both state and input delays. This stands in contrast to the majority of existing studies that primarily focus on input delays alone. We support our theoretical framework with a simulation example to illustrate its effectiveness.