Exponential Stabilization for Interconnected Time-Delay Systems

Abstract

Decentralized exponential stabilization 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, 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.