Design of Nonlinear State Observers for One-Sided Lipschitz Systems
For control theorists, it relaxes the restrictive Lipschitz condition, enabling observer design for a wider class of nonlinear systems.
This paper extends state observer design to one-sided Lipschitz systems, a broader class than standard Lipschitz systems, and provides a solution via linear matrix inequalities, reducing conservativeness.
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.