This thesis is divided into two main parts. The contribution of the first part is to design a continuous-time Piecewise-Affine (PWA) observer for a class of nonlinear systems. It is shown that the state estimation error is ultimately bounded. The bound on the state estimation error depends on the PWA approximation error. Moreover, it is shown that the state estimation error is still convergent and ultimately bounded when the output of the system is only available at sampling instants. The proof of convergence is presented in two parts: conditions dependent on the sampling time and conditions independent of the sampling time. In addition, ultimate boundedness of the state estimation error is proven in the presence of norm bounded measurement noise. It is shown that the bound on the state estimation error is dependent on the sampling time, PWA approximation error and the bound on the norm of the noise. The proposed approach for observer design leads to a convex optimization which can be solved efficiently using available software packages.

The contribution of the second part is to implement the proposed PWA observer on a real setup of a wheeled mobile robot (WMR) available at the Hybrid Control Systems (HYCONS) Laboratory of Concordia University. Although some researchers have applied different types of observers to experimental applications, practical implementation of PWA observers has not been given much attention by researchers. In this thesis for the first time a PWA observer is applied to the WMR. The WMR is an example of a nonlinear system with a sampled output in the presence of measurement noise. The results of the experimental implementation validate the proposed theoretical results in the first part.