Stabilizability of multiple time-delay overlapping systems: The inclusion principle approach

In this paper, a sufficient delay-dependent condition for the stabilization of overlapping linear continuous-time uncertain systems with multiple delays by robust overlapping output feedback controllers is given. The overlapping system is first expanded into a higher dimensional system (expanded system) where the overlapping subsystems appear as disjointed from each other. Then, robust local delay-dependent output feedback controllers, for disjoint subsystems, are designed, using a Linear Matrix Inequality (LMI) based iterative algorithm. Finally, the designed local controllers are contracted to an overlapping controller to be implemented on the original system. The preservation of stability and performance through contraction is proven. The design approach is applied to the Load Frequency Controller (LFC) of an uncertain, state-delayed, 2-area interconnected power system with overlapping parts.