Output feedback variable structure control design with an H2H2 performance bound constraint

In this paper, we give an LMI-based method for designing an output feedback variable structure control (VSC) system with an H2H2 constraint. The uncertain system model under consideration may have nonmatching disturbance input signals. Nonmatching disturbance input signal reduction is performed via H2H2 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 H2H2 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 H2H2 constraint. Finally, by using a design example we show that our method can supplement the existing results.