Robust Stabilization of Nonlinear Time Delay Systems Using Convex Optimization

We address the problem of robust, global, delay-dependent and delay-independent stabilization of nonlinear time-delay systems with memory state feedback. The methodology we use is based on a linear-like representation of the time-delay system for which we construct appropriate Lyapunov-Krasovskii functionals. The resulting conditions take the form of infinite-dimensional state-dependent Linear Matrix Inequalities which can be treated as sum of squares matrices. The sum of squares program that emerges can then be solved using semidefinite programming and SOSTOOLS, which results in an algorithmic construction of the control law and the Lyapunov-Krasovksii functional. An example is presented that shows the effectiveness of the methodology.