Sliding mode control for A class of bilinear systems

This paper considers the design of an augmented sliding mode control (SMC) to stabilize a class of uncertain bilinear systems. The design of a classical SMC is shown to suffer from a singularity problem. The singularity is overcome by augmenting the classical SMC with an auxiliary control law. The proposed control law is shown to drive the system trajectories to the sliding manifold and to maintain them there for all subsequent time, therefore, ensuring the asymptotic stability of the closed-loop system.