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.