Decentralized Mixed Delay-Dependent/Delay-Independent Stabilization of Interconnected Time-Delay Systems

The problem of decentralized stabilization of interconnected systems that are delay-dependent for some delays and delay-independent for the remaining ones is addressed in this paper. For the purpose, some of the subsystems are grouped to form new larger subsystems. Such a grouping allows all the interconnection delays present among the smaller subsystems to be divided into two groups in the new subsystem description — (i) intraconnection delays, within the larger subsystem, and (ii) interconnection delays, among the larger subsystems. This facilitates delay-dependent stabilization for the intraconnection delays and delay-dependent stabilization for the interconnection delays. An LMI based stabilization criterion is derived for such mixed delay-dependent/delay-independent stabilization of the overall system. A numerical example is presented demonstrating the effectiveness of the developed criterion.