This paper presents a method to design sliding mode observers for a class of uncertain systems using linear matrix inequalities. The objective is to exploit the degrees of freedom available in the design which have hitherto been ignored because of the lack of a tractable solution framework. The relationship between the linear component of the sliding mode observer and a particular sub-optimal observer arising from classical linear quadratic Gaussian (LQG) theory is demonstrated. This helps motivate how the design weighting matrices inherent in the method may be chosen in practice. It will also be shown how the weighting matrices affect the dynamics of the sliding motion. Furthermore, using pole-placement and pole clustering methods, the poles of the sliding motion can be forced to lie in a specified region in the complex plane, so that the performance of the sliding motion can be tuned. This paper will also present a more general solution where the eigenvalues of the linear part of the observer are forced to lie in a specified region.