Control and synchronizing nonlinear systems with delay based on a special matrix structure

This work presents a direct approach to design stabilizing controller for nonlinear systems with delay based on a special matrix structure and proves the validity of the approach according to Lyapunov–Krasovskii stable theorem and Linear Matrix Inequality—LMI. Control Lorenz system and synchronizing Rössler system with delay are taken as examples to explain the approach. Numerical simulations confirm the effectiveness of the approach proposed.