Delay‐Scheduled Adaptive Observer Control Strategy for Nonlinear Systems With Time‐Varying Delays

ABSTRACT This paper presents a delay‐scheduled control framework with an adaptive observer for stabilizing nonlinear systems subject to unknown bounded time‐varying input delays and disturbances. The method employs a Lyapunov–Krasovskii functional incorporating the true delay and its real‐time estimate, combined with a convex design procedure based on linear matrix inequalities to ensure closed‐loop stability and prescribed H Infinity performance. Unlike fixed‐delay controllers that suffer from temporal mismatches or neural‐network methods with high computational costs, this approach utilizes an adaptive observer to estimate instantaneous delay and schedule controller gains accordingly. The parameters are obtained through a decoupled, computationally tractable two‐step design. The framework's effectiveness is demonstrated via simulations of the 3D Lorenz and 4D hyperchaotic Lü systems. Comparative analysis confirms the delay‐scheduled controller outperforms benchmarks like adaptive neural dynamic surface control and predefined‐time sliding mode strategies. Specifically, the method achieves a 16% –22% reduction in integral absolute error compared to recent adaptive neural schemes, while delivering superior energy efficiency and eliminating control chattering. These results prove the strategy provides a robust, low‐complexity solution for time‐varying delay compensation, achieving the lowest tracking errors and H Infinity disturbance attenuation levels among the evaluated methods.