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This paper focuses on the observer-based <inline-formula> <tex-math notation="LaTeX">$H_\infty $ </tex-math></inline-formula> control issue for large-scale systems under denial-of-service attacks. Due to the security vulnerability of communication networks, adversaries have the capability to hamper the system normal operation by blocking the signal exchange in both sensor-to-observer channels and the observer-to-observer channels. Under this scenario, a decentralized proportional-derivative-like controller is employed to realize the predetermined <inline-formula> <tex-math notation="LaTeX">$H_\infty $ </tex-math></inline-formula> performance while considering the improvement of dynamic response of closed-loop systems. By using the Lyapunov stability theory, a sufficient condition dependent on the attack occurring probability is established to realize the desired control performance. Furthermore, in light of the established condition, the desired controller and observer gains are formalized by resorting to the orthogonal decomposition of control matrix. Finally, the effectiveness and practicability of the control scheme are illustrated by resorting to the numerical simulation of a four area power system.