Asymptotic stability of time delay systems with unknown uncertainty bounds using adaptive robust control

The problem of adaptive robust control of uncertain linear systems with multiple time delays in the state variables is considered in this paper. The essential requirement for the parameter uncertainties is that they satisfy some matching conditions and are norm bounded, whose bounds are unknown. The objective is to design an adaptive robust controller based on a new Lyapunov Krasovskii functional such that the closed loop system is asymptotically stable. The proposed design condition is formulated in terms of linear matrix inequality (LMI) which can be easily solved by LMI Toolbox in Matlab. Finally, two numerical examples are included to illustrate the effectiveness of the derived controller.