A novel event-triggered nonlinear control approach for descriptor systems with time-varying delay and input saturation constraints

This paper addresses the pressing challenge of controlling descriptor systems with interval time-varying delays and input saturation constraints—an area of critical importance yet limited exploration in the control literature. Such systems pose unique difficulties due to the singularity of their state-space representation, complex delay structures, and actuator limitations. To tackle these challenges, we propose a novel nonlinear event-triggered control strategy for delayed descriptor systems. The controller integrates an event-triggering mechanism to reduce communication load while ensuring enhanced transient performance, even in the presence of actuator saturation. A composite design combining linear and nonlinear control components is employed: the linear part guarantees closed-loop stability and output tracking, whereas the nonlinear part actively improves transient response characteristics, such as reducing overshoot and smoothing the output response under input constraints. Rigorous admissibility analysis—encompassing stability, regularity, and impulse-freeness—is conducted using a carefully constructed Lyapunov-Krasovskii functional. Furthermore, delay-range-dependent conditions are derived in the form of linear matrix inequalities (LMIs), leading to reduced conservatism compared to traditional techniques. Zeno-freeness is also ensured by explicitly deriving a lower bound on inter-event times. Extensive comparative simulations validate the theoretical findings and demonstrate the superior performance of the proposed approach relative to conventional control methods.