Exponential Reduced-Order Observers for Nonlinear Systems Satisfying Incremental Quadratic Constraints

This paper considers the design problem of exponential reduced-order observers for nonlinear systems satisfying incremental quadratic constraints governed by an incremental multiplier matrix. Sufficient existence conditions of the exponential full-order observers are established and formulated in terms of matrix inequalities. Then, it is shown that the conditions under which an exponential full-order observer exists also guarantee the existence of an exponential reduced-order observer. Moreover, with a proper parameterization of the multiplier matrix, the design of reduced-order observers is reduced to solving linear matrix inequalities of the Lyapunov matrix and observer gain matrices. Finally, the effectiveness of the proposed design method is illustrated by an example.