Output feedback variable structure control design with an H₂ performance bound constraint

In this paper, we give an LMI-based method for designing an output feedback variable structure control (VSC) system with an H₂ constraint. The uncertain system model under consideration may have nonmatching disturbance input signals. Nonmatching disturbance input signal reduction is performed via H₂ norm minimization. In terms of a constrained Riccati inequality we give a sufficient condition for the existence of a linear sliding surface and a compensator guaranteeing an H₂ constraint, and we show that the control parameters can be characterized by using the solution to the given inequality condition. We also give a simple LMI-based design algorithm of an output feedback VSC law guaranteeing an H₂ constraint. Finally, by using a design example we show that our method can supplement the existing results.