Semidefinite Programming Methods of Ascertaining Stability for a Nonlinear Delay System Subject to Constraints

This paper deals with stability problem for nonlinear delay systems. The proposed approach is based on the assumption that on a subset of instant states the system is represented by a continuous-time Takagi– Sugeno system with delay. The aim of the study is to present sufficient conditions of stability for the system subject to the constraints defining the subset under consideration. Because of the constraints, another important issue is how to estimate the set of initial points such that the trajectories starting at those points remain to satisfy the constraints. Using Lyapunov functions with the Razumikhin conditions, we obtain stability conditions and an estimation of the domain of attraction in terms of linear matrix inequalities with scalar parameters. The obtained problems can be formulated by semidefinite programming and solved numerically.