Static State and Output Feedback Synthesis for Time-Delay Systems*

In this paper, the design of a static feedback gain for a linear system subject to an input delay is studied. This synthesis is based on a stability analysis conducted using Lyapunov-Krasovskii theorem and Bessel-Legendre inequalities. It is expressed in terms of linear matrix inequalities. Some bilinear non-convex matrix inequalities are obtained to go from analysis to synthesis. They are then difficult to solve and an iterative procedure is given which takes advantage of the elimination lemma. Naturally, slack variables are introduced and values coming from an optimization process are proposed to reduce the conservatism. The two main corollaries discuss the static state and output feedback synthesis. Finally, a comparison is proposed and shows that this formulation introduces small conservatism.

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