LMI optimization approach to asymptotic stability of certain neutral delay differential equation with time-varying coefficients

In this article, a stability criterion for all solutions of a class of neutral equation of the formddt[x(t)+c(t)x(t−τ)]+p(t)x(t)+q(t)x(t−σ)+r(t)∫t−δtx(s)ds=0to approach zero at t→∞ is presented. Using the Lyapunov method, the condition, which is expressed in terms of linear matrix inequality, is delay-dependent and can be easily solved by various efficient convex optimization algorithm.