A numerical method for feedback stabilization of linear delay systems with applications

This paper is concerned with the feedback stabilization for linear delay systems. We apply the modified Polak-Ribiere-Polyak (NPRP) conjugate gradient method to the numerical algorithm for the feedback stabilization of linear delay systems. Convergence conditions are obtained without the convexity assumption when the line search fulfills the Wolfe conditions or the Armijo condition. The numerical algorithm based on the NPRP method is applied to solve the feedback stabilization problem of combustion chamber systems in liquid propellant rocket motors. The numerical example shows that the numerical algorithm based on the conjugate gradient method is faster than the one based on the quasi-Newton method.