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This paper addresses the static output feedback (SOF) Hinfin control for continuous-time linear systems with an unknown input delay from a novel perspective. New equivalent characterizations on the stability and Hinfin performance of the closed-loop system are established in terms of nonlinear matrix inequalities with free parametrization matrices. These delay-dependent characterizations possess a special monotonic structure, which leads to linearized iterative computation. The effectiveness and merits of the proposed approach are shown through numerical examples.