On the need for switchedgain observers for nonmonotonic nonlinear systems Abstract   This paper focuses on the challenges in observer design for nonlinear systems which are nonmonotonic. A class of nonlinear systems is considered in which the process dynamics and output equations are both composed of nonlinear vector functions of scalar combinations of the states. The nonlinear functions are assumed to be differentiable with bounded derivatives. An observer design algorithm that requires solving just a single linear matrix inequality for exponentially convergent state estimation is developed. The developed algorithm works effectively when the involved nonlinear functions are monotonic. However, it fails when all or even some of the system functions are nonmonotonic. Both numerical computation and analytical results show that the observer design LMI has no feasible solutions when either all output functions or all process dynamics functions are nonmonotonic. Further, other constant gain LMIbased observer design methods from literature also fail when the involved nonlinear functions are all nonmonotonic, no matter how small the Lipschitz constant or the Jacobian bounds of the nonlinearities. This limitation has not previously been recognized in observer design literature. To overcome this limitation, a hybrid observer that switches between multiple constant observer gains is developed that can provide global asymptotic stability for systems with nonmonotonic nonlinear functions. Hybrid observers with switched gains enable existing observer design methods to be utilized for nonmonotonic nonlinear functions with finite local extrema. The application of the developed hybrid observer to two motion estimation applications, one a vehicle position tracking problem on roads and another a piston position estimation problem for an industrial actuator, are demonstrated.

Continuousdiscrete time observers for a class of MIMO nonlinear systems In this paper, we investigate the possibility of designing an observer for a class of continuoustime dynamical systems with nonuniformly sampled measurements. More specifically, we propose an observer with a time varying gain witch converges exponentially under some conditions on the sampling partition diameter. The proposed observer is an impulsive system since it is described by a set of differential equations with instantaneous state impulses corresponding to the measured samples and their estimates. As it is customarily done in the literature, we show that such an impulsive system can be split into two subsystems and be put under the form of a hybrid system which is designed using a continuoustime observer together with an intersample output predictor. Simulations results involving a typical bioreactor are given to show the effectiveness of the proposed observer.