Asynchronous Gain-Scheduling Secure Control of Nonlinear Cyber-Physical Systems Under Complex Transition Probabilities: A Dual-Domain Polynomial Framework

This article proposes an asynchronous gain-scheduling secure control framework for nonlinear cyber-physical systems subject to complex and uncertain mode transition behaviors. To address the challenge that ideal probabilistic information is often unavailable in practical industrial environments, a dual-domain polynomial methodology is developed to enhance control performance under realistic conditions. In the structural domain, complex transition probabilities—comprising imprecise and partially unknown components—are reconstructed into a polytopic form, enabling a flexible and accurate abstraction of stochastic system dynamics. In the control design domain, homogeneous polynomial Lyapunov functions and controller structures are utilized to reduce conservatism and improve robustness. The proposed method guarantees exponential mean-square stability and desired performance under cyber attacks. Numerical simulations and hardware-in-the-loop (HIL) experiments on a nonlinear active suspension system confirm the superiority of the approach in terms of feasible design region and performance $\gamma _{\min }$ optimization of at least 32.4%.