Observer-Based Security Control for 2-D Fuzzy Switched Systems With Nonhomogeneous Sojourn Probabilities

Abstract

This article proposes a novel framework of nonhomogeneous sojourn probabilities in the 2-D domain and investigates the observer-based security control issue for 2-D fuzzy switched systems (SS) under an adaptive-threshold-based saturation function. In comparison with the existing homogeneous/nonhomogeneous Markov processes, the proposed nonhomogeneous sojourn probability framework enhances measurability and reduces computational complexity, making it a more reasonable approach. The security control challenge for 2-D fuzzy SS is addressed in the context of randomly occurring attacks with uncertain occurrence rates, where the uncertainty is norm-bounded and asymmetrical around the nominal rate. To mitigate the effects of these abnormal attacks, a novel adaptive-threshold-based saturation function is employed, ensuring that transmitted information remains within an acceptable range. Leveraging Lyapunov theories, sufficient conditions are attained to guarantee the asymptotically mean square stable with noise attenuation performance. The validity of the proposed theoretical results is demonstrated through a simulation example.