Robust Control for Multiple Time Delay MIMO Systems with Delay - Decouplability Concept

In this paper, we consider linear time-invariant minimum phase MIMO plants with multiple control delays. The time delays appear at several components of the state. The delay decoupling control (DDC) aims to force the characteristic equation to facilitate the assessment of stability in each of the delays, independently from one another (thus introducing “delay decouplability”). When, however, some system parameters are uncertain, the corresponding characteristic equation exhibits truly coupled delays, which brings the stability assessment problem into N-P hard complexity class. This operation can still be very efficient using a recent paradigm called the Cluster Treatment of Characteristic Roots (CTCR). The main contribution of this study is to show that, for a class of uncertain time-delayed dynamics, if the feedback control is properly designed, decouplability may still hold, consequently the robustness analysis can be performed efficiently. This result is demonstrated for a 2-input, 2-output system, and it is claimed that the findings are scalable to higher dimensional dynamics. An example case study of a cart-pendulum system is examined, considering varying parametric uncertainties.