H ∞ Observer Design for Descriptor Systems with Slope‐Restricted Nonlinearities

This paper considers the H ∞ observer design problem for a class of nonlinear descriptor systems subject to disturbances. A linear matrix inequality (LMI)‐based observer design method is derived such that the error system is internally exponentially stable with a given decay rate and the L 2 gain of the mapping from the disturbances to the error output is less than or equal to a prescribed level. It is further shown that the solution to the obtained observer system exists and is unique for any compatible initial condition. Two convex optimization problems are formulated to improve the estimation performance. The obtained results are illustrated by numerical examples. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society