State feedback redesign for PWA system with regional pole placement performance using LMI

This paper considers a state-feedback controller which guarantees the stability of a class of nonlinear systems over the desired region and ensures some practical performance criteria of the closed-loop system. We apply the piecewise affine technique together with the regional pole placement and linear quadratic regulator in order that all design formulations are cast as a linear matrix inequality (LMI) optimization problem. Moreover, the discrete-time controller is also obtained from the continuous-time controller via LMI approach. The numerical example has been provided and we apply the proposed method to the bicycle control using gyroscopic stabilization. The simulation result shows that the obtained controller gain can stabilize the original nonlinear system perfectly under the required specification.