Observer design for one-sided Lipschitz descriptor systems

This paper describes the design of a nonlinear observer for a class of nonlinear descriptor systems with one-sided Lipschitz nonlinearities. To provide a general framework applicable to a large class of systems, nonlinearities and disturbances are considered at the state as well as at the output equations. Non-strict and strict bilinear matrix inequality (BMI)-based robust observer synthesis schemes are provided by utilizing the one-sided Lipschitz condition, the concept of quadratic inner boundedness, the generalized Lyapunov theory for singular systems, and the L₂ gain reduction. The BMI-based condition is converted into the linear matrix inequality (LMI)-based condition by utilizing change of variables for straightforward computation of the observer gain matrix. In contrast to the traditional observer schemes for one-sided Lipschitz nonlinear systems, the resultant scheme is applicable to singular systems, capable of dealing with nonlinearities at the output equation and appropriate for treating with disturbances. Two simulation examples for the one-sided Lipschitz and the singular one-sided Lipschitz nonlinear systems are provided to validate the proposed observer synthesis methodologies.