and Gerhard Nygaard

In dealing with a large-scale system, one usually does not have adequate knowledge of the plant parameters and interactions among subsystems. The decentralized adaptive technique, designed independently for local subsystems and using locally available signals for feedback propose, is an appropriate strategy to be employed. In the context of decentralized adaptive control, a number of results have been obtained, see for examples Ioannou (1986); Narendra & Oleng (2002); Ortega (1996); Wen (1994). Since backstepping technique was proposed, it has been widely used to design adaptive controllers for uncertain systems Krstic et al. (1995). This technique has a number of advantages over the conventional approaches such as providing a promising way to improve the transient performance of adaptive systems by tuning design parameters. Because of such advantages, research on decentralized adaptive control using backstepping technique has also received great attention. In Wen & Soh (1997), decentralized adaptive tracking for linear systems was considered. In Jiang (2000), decentralized adaptive tracking of nonlinear systems was addressed, where the interaction functions satisfy global Lipschitz condition and the proposed controllers are partially decentralized. In Wen & Zhou (2007); Zhou & Wen (2008a;b), systems with higher order nonlinear interactions were considered by using backstepping technique. Stabilization and control problem for time-delay systems have received much attention, see for examples, Jankovic (2001); Luo et al. (1997); Wu (1999), etc. The Lyapunov-Krasovskii method and Lyapunov-Razumikhin method are always employed. The results are often obtained via linear matrix inequalities. Some fruitful results have been achieved in the past when dealing with stabilizing problem for time-delay systems using backstepping technique. In Ge et al. (2003), neural network control cooperating with iterative backstepping was constructed for a class of nonlinear system with unknown but constant time delays. Jiao & Shen (2005) and Wu (2002) considered the control problem of the class of time-invariant large-scale interconnected systems subject to constant delays. In Chou & Cheng (2003), a decentralized model reference adaptive variable structure controller was proposed for a large-scale time-delay system,where the time-delay function is known and linear. In Hua et al. (2005), the robust output feedback control problem was considered for a class of nonlinear time-varying delay systems, where the nonlinear time-delay functions are bounded by known functions. In Shyu et al. (2005), a decentralized state-feedback variable structure controller was proposed for large-scale systems with time delay and dead-zone nonlinearity. However, in Shyu et al. (2005), the time delay is constant and the parameters of the dead-zone are Decentralized Adaptive Stabilization for Large-Scale Systems with Unknown Time-Delay 7