A new robust nonfragile controller design scheme for a class of hybrid systems through piecewise affine models (Q1720493)

Summary: This paper investigates the robust \(\mathcal{H}_{\infty}\) nonfragile control problem for a class of discrete-time hybrid systems based on piecewise affine models. The objective is to develop an admissible piecewise affine nonfragile controller such that the resulting closed-loop system is asymptotically stable with robust \(\mathcal{H}_{\infty}\) performance \(\gamma \). By employing a state-control augmentation methodology, some new sufficient conditions for the controller synthesis are formulated based on piecewise Lyapunov functions (PLFs). The controller gains can be obtained via solving a set of linear matrix inequalities. Simulation examples are finally presented to demonstrate the feasibility and effectiveness of the proposed approaches.