Robust Control for Multiple Time Delay Systems With Delay–Decouplability Concept

We consider linear time-invariant minimum phase MIMO plants in this paper, with multiple control delays. The delays appear at several components of the state. Deployment of delay decoupling control (DDC) creates a characteristic equation which facilitates the assessment of stability in each of the delays independently from each other. When, however, some system parameters are uncertain, the characteristic equation seems to entail truly coupled delays, which forces the stability assessment to an N-P hard complexity class problem. We show that this assessment can be very efficient using the Cluster Treatment of Characteristic Roots (CTCR) paradigm. The main contribution of the study is for a certain class of structures, if the feedback control forms with independent delays on separate feedback channels decouplability may still hold, and the robustness analysis becomes efficient. This result is demonstrated for 2-input, 2-output system, and it is claimed that the findings are scalable to higher dimensional dynamics. Example case study of a cart-pendulum system is treated.