  Control and state estimation of nonlinear systems satisfying a Lipschitz
continuity condition have been important topics in nonlinear system theory for
over three decades, resulting in a substantial amount of literature. The main
criticism behind this approach, however, has been the restrictive nature of the
Lipschitz continuity condition and the conservativeness of the related results.
This work deals with an extension to this problem by introducing a more general
family of nonlinear functions, namely one-sided Lipschitz functions. The
corresponding class of systems is a superset of its well-known Lipschitz
counterpart and possesses inherent advantages with respect to conservativeness.
In this paper, first the problem of state observer design for this class of
systems is established, the challenges are discussed and some analysis-oriented
tools are provided. Then, a solution to the observer design problem is proposed
in terms of nonlinear matrix inequalities which in turn are converted into
numerically efficiently solvable linear matrix inequalities.
