Abstract:

In nonlinear cyber-physical systems(CPS), random switching behaviors and nonlinear characteristics often coexist, while complex transition probabilities and cyber attacks further threaten system safety and stability. This paper proposed a secure gain-scheduling method for stochastic nonlinear CPS based on dual-domain polynomial framework. This method was constructed by integrating fuzzy modeling with Markov jump systems, which enabled accurate characterization of nonlinear dynamics and stochastic switching phenomena. A polytopic reconstruction strategy in the structural domain was introduced to transform imprecise and partially unknown transition probabilities into a tractable form, thereby avoiding infeasibility under complex probabilistic environments. In the control design domain, homogeneous polynomial Lyapunov functions and controller structures were employed to effectively reduce conservatism and enhance robustness. Theoretical analysis results indicate that the proposed method guarantees exponential mean-square stability and performance optimization even under denial-of-service attacks and other cyber threats. Numerical simulations further verify the effectiveness of the proposed approach, showing its superiority in expanding the feasible solution domain and improving performance indices. The results provide a practical solution for secure control of CPS operating under complex probabilistic and adversarial conditions.

Key words: CPS, Markov jump system, fuzzy system, DoS attack