The author considers a system described by a neutral functional differential equation
with a controllable pair. To this system he associates the quadratic cost function
where , and is the initial condition. The paper aims to find a control law such that the resulting closed-loop system is exponentially stable with guaranteed quadratic cost , where is some number. The paper relies on the choice of a quadratic Lyapunov functional leading finally to some Linear Matrix Inequalities whose feasibility guarantees the problem’s solution.