Adaptive robust control of uncertain systems with state and input delay

In this paper, adaptive robust control of uncertain systems with multiple time delays in states and input is considered. It is assumed that the parameter uncertainties are time varying norm-bounded whose bounds are unknown but their functional properties are known. To overcome the effect of input delay on the closed loop system stability, new Lyapunov Krasovskii functional will be introduced. It is shown that the proposed adaptive robust controller guarantees globally uniformly exponentially convergence of all system solutions to a ball with any certain convergence rate. Moreover, if there is no disturbance in the system, asymptotic stability of the closed loop system will be established. The proposed design condition is formulated in terms of linear matrix inequality (LMI) which can be easily solved by LMI Toolbox in Matlab. Finally, an illustrative example is included to show the effectiveness of results developed in this paper.