Exponential stability assignment of neutral delay-differential systems by a class of linear-quadratic regulators

A method to construct a simple feedback law for neutral delay-differential systems is proposed. The feedback gain is determined with a solution of a matrix inequality, which can be solved numerically via the technique of solving finite-dimensional linear matrix inequalities. It is shown that the resulting closed-loop system is asymptotically stable, and if some transformation of variables is introduced, it is assured to have a pre-assigned degree of exponential stability. Moreover, it belongs to a class of linear-quadratic regulators. The design procedure is demonstrated and the effectiveness of the feedback is evaluated with a numerical simulation.