This paper presents linear matrix inequality (LMI) conditions to design stabilizing state-feedback controllers for linear systems with distributed input delays. A LyapunovKrasovskii functional approach is used and the obtained parametric matrix inequalities are reformulated as LMIs using the full-block S-procedure and a convex hull relaxation. These LMI conditions can be used, for example, to design stabilizing controller for networked control systems (NCS). In this setup, the kernel of the distributed input delay describes the probability density of the packet-delay in the communication channel. This controller design for NCS is illustrated in an example.Index Terms-Time delay systems, distributed input delay, stabilization, full-block S-procedure, convex hull relaxation, networked control systems.

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