Exponential stabilization controller design for interconnected time delay systems

Decentralized robust control problem is investigated for a class of large scale systems with time varying delays. The considered systems have mismatches in time delay functions. A state coordinate transformation is first employed to change the original system into a cascade system. Then the virtual linear state feedback controller is developed to stabilize the first subsystem. Based on the virtual controller, a memoryless state feedback controller is constructed for the second subsystem. By choosing new Lyapunov Krasovskii functional, we show that the designed decentralized continuous adaptive controller makes the solutions of the closed-loop system exponentially convergent to a ball, which can be rendered arbitrary small by adjusting design parameters. Finally, a numerical example is given to show the feasibility and effectiveness of the proposed design techniques.