Sliding mode control using state/output feedback in hybrid systems

This paper presents sliding mode control using state/output feedback for linear hybrid systems. The sliding manifold is taken to be part of the switching hyperplane of the hybrid system and the conditions for the existence of sliding modes and for the stability of motion equation are formulated in the form of trilinear matrix inequalities (TMI). Observing that these TMI accept a special form, we are able to propose an algorithm that can use the existing software for the solution of linear matrix inequalities (LMI) to solve for the desired feedback gains. The concept is illustrated with an example.