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This paper presents a kind of controller design method for a class of networked control systems (NCSs) with multiple packet dropouts, where the number of consecutive packet dropouts is limited by a known upper bound. A novel model that can be used to describe multiple packet dropouts in both sensor-to-controller and controller-to-actuator sides is provided. A sufficient condition for mean-square asymptotic stability is derived for the closed-loop networked control system, which is dependent on the upper bound of the packet dropouts number. The corresponding state feedback control law is presented in terms of linear matrix inequalities (LMIs). A networked control system for an inverted pendulum is finally provided to show the effectiveness and applicability of the proposed method.