A robust Sliding Mode Controller for a class of SISO bilinear delayed systems

In this paper we propose a Sliding Mode Controller for a class of scalar bilinear systems with delay in both the input and the state. Such a class is considered since it has shown to be suitable for modelling and control of a class of turbulent flow systems. The stability and robustness analysis for the reaching phase in the controlled system are Lyapunov-based. However, since the sliding dynamics is infinite dimensional and described by an integral equation, we show that the stability and robustness analysis is simplified by using Volterra operator theory.