Piecewise affine model approximation for unmanned bicycle

This paper presents the methods of how to approximate the nonlinear dynamic system into the Piecewise affine state-space model and an application to controller synthesis based on Piecewise Quadratic stability criterion. Apart from linearization technique, three other methods based on minimizing least-square error have been observed. The average of root mean square error in each affine region is considered as a model selection criteria. Controller design using this approximated PWA model is made through Piecewise Quadratic as an LMI problem. These controller gains are finally simulated in the original nonlinear model comparing with the approximated PWA model to verify its validity. The unmanned bicycle with gyroscopic flywheel is selected to illustrate the whole idea in this paper.