Non-fragile state-feedback control of uncertain piecewise-affine slab systems with input constraints: a convex optimisation approach

The main contribution of this work is to propose a design technique for state-feedback control of continuous-time piecewise-affine (PWA) systems that is robust not only to the system uncertainties, but also to variations of the controller gains. More specifically, this study presents sufficient conditions to synthesise a robust non-fragile PWA controller that exponentially stabilises the closed-loop equilibrium point. Furthermore, these conditions are cast as an optimisation problem subject to a set of linear matrix inequalities (LMIs), which can then be solved efficiently. In addition, a set of LMI conditions are derived to ensure that the control input will always meet a pre-assigned upper bound. Simulation results demonstrate the effectiveness of the proposed approach.