Synthesis of stabilizing antiwindup controllers using piecewise quadratic Lyapunov functions

We consider the problem of antiwindup controller synthesis based on the general antiwindup framework presented in Kothare et al. (Automatica, vol. 30, no. 12, pp. 1869-1883, 1994) applicable to linear time-invariant systems (LTI) subject to a saturating actuator. Our synthesis approach takes advantage of the fact that the antiwindup system is a piecewise affine system and thus, we can utilize piecewise quadratic Lyapunov function theory Johansson and Rantzer (IEEE Trans. Autom. Control, vol. 43, no. 4, pp. 555-559, Apr. 1998), Rantzer and Johansson (IEEE Trans. Autom. Control, vol. 45, no. 4, pp. 629-637, Apr. 2000), and Johansson (Proc. 14th World Congr., Beijing, China, 1999, pp. 521-5260) to determine a stabilizing antiwindup control law. The synthesis problem is expressed in terms of bi-linear matrix inequalities (BMIs) and is solved using an iterative approach as well as using commercial software. The performance of the system is optimized by minimizing an upper bound on the induced L-2 gain of the system. The proposed approach is demonstrated using examples.