Uncertain homogenous bilinear systems: a variable-structure control approach

This paper considers the design of a sliding mode control (SMC) to stabilize a class of uncertain homogenous bilinear systems. A new approach based on the concept of integral sliding mode is proposed along with an auxiliary control law to overcome the key problems associated with using the classical SMC for such systems. The design is robust with respect to a family of conically bounded perturbations in the sense that it ensures reachability of the sliding manifold as well as asymptotic closed-loop stability in the presence of any perturbation belonging to the uncertainty family