Robust control of uncertain systems with input delay and input sector nonlinearity

In this paper, we investigate a robust control method for some nonlinear control problems with an input delay. By letting input nonlinearity in the sector bounds as a new diagonal structured uncertainty, we transform the control problems with input nonlinearity into the robust control problems of linear systems with only structured uncertainty. Applying this idea, we obtain linear matrix inequality (LMI) conditions for delay-dependent robust stabilization of structured uncertain systems with input delay and input sector nonlinearity. In addition to LMI for the fixed input nonlinearity, we also propose an iterative LMI optimization algorithm to find robust input sector bounds such that the given uncertain system is stable for any input nonlinearity in these sector bounds