Multivariable anti-windup controller synthesis using bilinear matrix inequalities

We consider the problem of multivariable anti-windup bumpless transfer (AWBT) controller synthesis based on the general AWBT framework presented in (M.V. Kothare et al., Automatica 1994; 30(12): 1869-1883). We review several recent AWBT synthesis techniques. Next, we give a completely general formulation of the A WBT controller synthesis problem and show how this problem can be solved in terms of bilinear matrix inequalities (BMIs). For two simple examples, we demonstrate that an induced L₂ norm objective function is a sufficient performance indicator. Moreover, the objective minimum leads to multiple solutions for the static output feedback AWBT parameters, all of which provide equivalent output responses and graceful performance degradation under saturation. We also demonstrate the superior performance of the two parameter framework over an otherwise equivalent one parameter framework.