This paper addressed the problem of observer-based memory state feedback control design for semi-Markovian jump systems subject to input delays and external disturbances, where the measurement output was vulnerable to randomly occurring cyber attacks. To facilitate analysis, the cyber attacks were described by a nonlinear function that meets Lipschitz continuity and the possible attack scenarios were represented by a stochastic parameter that follows the Bernoulli distribution. Based on the information from the considered system and state observer, an augmented closed loop system was constructed. Then, by using the Lyapunov stability theory, an extended Wirtinger's integral inequality and stochastic analysis, the required stability criterion was proposed in the form of linear matrix inequalities. As a result, the control and observer gain matrices were efficiently derived, ensuring the stochastic stability of closed-loop systems with $H_{\mathrm{\infty }}$ performance, regardless of cyber attacks. To demonstrate the effectiveness and theoretical value of the proposed robust memory state feedback control design, simulation results were presented.

The asymptotic synchronization problem of chaotic Lur'e systems in the master-slave framework was explored in this paper. A time-varying delay feedback controller with quantization considerations and a delay-product-type Lyapunov-Krasovskii functional technique were employed to tackle this problem. Consider an error system based on master and slave systems, for which sufficient asymptotic stability requirements are developed to assure that the addressed system achieves proper synchronization. Following that, the desired control gain was determined by finding a feasible solution to these stability requirements. The results of this paper were validated using a numerical example with simulations, which revealed that they were superior to previously published ones.