Observerbased strict positive real (SPR) feedback control system design This paper presents theory for stability analysis and design for a class of observerbased feedback control systems. Relaxation of the controllability and observability conditions imposed in the YakubovichKalmanPopov (YKP) lemma can be made for a class of nonlinear systems described by a linear timeinvariant system (LTI) with a feedbackconnected conebounded nonlinear element. It is shown how a circlecriterion approach can be used to design an observerbased state feedback control which yields a closedloop system with specified robustness characteristics. The approach is relevant for design with preservation of stability when a conebounded nonlinearity is introduced in the feedback loop. Important applications are to be found in robotics (force control) and nonlinear control in hybrid control. Copyright (C) 2001 IFAC. (Less)

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.