Abstract :
In this paper, we investigate the stability problems of large scale integrodifferential systems. The basic idea is first to decompose a large scale system into several appropriate lower order subsystems. Neglecting the interconnection among them, we obtain several isolated subsystems. For each subsystem, a simple method is used to construct a Lyapunov functional to characterize its stability properties. These Lyapunov functionals are then employed in the construction of the Lyapunov functional for the overall system. Unlike ordinary differential systems, simple linear combination of the Lyapunov functional obtained through the stability analysis of the isolated subsystems is no longer a good candidate for the overall integrodifferential system. To overcome this difficulty, we modify the well-known decomposition-aggregation method used for ordinary differential systems and successfully construct, incorporating the special structure of the integral part, the Lyapunov functional or the overall integrodifferential system. Several stability criteria are then established through various aggregation techniques. Since the present approach is constructive, it may be more useful in applications.
