On the robustness of multivariable algebraic loops with sector nonlinearities

The paper is motivated by multivariable 'anti-windup' schemes. Such schemes are often described in a form that includes a multivariable algebraic loop. Multivariable algebraic loops may be particularly problematic in terms of well-posedness (the existence and uniqueness of the solutions) and robust stability. Conditions for well-posedness of such loops have been analysed previously. Here we extend this analysis to consider robust stability of the algebraic loop with small time-delays. It is shown that sufficient conditions for robustness of the algebraic loop can be directly incorporated into an LMI based static anti-windup controller synthesis. In addition, an alternative implementation of the algebraic loop is shown to have robustness without altering the LMI set up.