In this work, an alternative for sliding surface design based on linear and bilinear matrix inequalities is proposed. The methodology applies for reduced and integral sliding mode control, both continuous- and discrete-time; it takes advantage of the Finsler's lemma to provide a greater degree of freedom than existing approaches for sliding subspace design. The sliding surfaces thus constructed are systematically found via convex optimization techniques, which are efficiently implemented in commercially available software. Examples are provided to illustrate the effectiveness of the proposed approach.
sliding mode control, linear matrix inequalities, variable structure, sliding subspace design
93B12, 90C25, 51M16