Synthesis of stabilizing anti-windup controllers using piecewise quadratic Lyapunov functions

We consider the problem of multivariable anti-windup bumpless transfer (AWBT) controller synthesis based on the general AWBT framework presented in [6]. Specifically, we propose a method for synthesizing AWBT compensators which stabilize linear, time-invariant systems (LTI) subject to saturating actuators. Our synthesis approach takes advantage of the fact that the AWBT system is a piecewise affine system and thus, we can utilize piecewise quadratic Lyapunov function theory [5, 10, 4] to determine a stabilizing control law. The synthesis problem is solved via iteration between a set of linear matrix inequalities (LMIs). The utility of the approach is demonstrated on a simple example where our method is shown to be less conservative.