Observer and output feedback stabilisation for a class of nonlinear systems

Abstract

The objective of the work is twofold. First, we investigate the problem of observer design for a class of systems in cascade form. We suppose that an observer exists for each subsystem and then prove that this interconnection is an observer for the overall system. One of both nonlinear functions is assumed to be not Lipschitz (e.g. to satisfy a quadratic constraint on the unmeasured part of the state). This first main result may be viewed as an improvement of Besançon and Hammouri (Besançon, G., and Hammouri, H. (1998), ‘On Observers Design for Interconnected Systems’, Journal of Mathematical Systems, Estimation and Control, 8, 377–380) in which the authors discussed the problem of the synthesis of interconnected observers. The second part is a generalisation of Ammar, Mabrouk, and Vivalda (Ammar, S., Mabrouk, M., and Vivalda, J.-C. (2009), ‘Observer and Global Output Feedback Stabilisation for Some mechanical Systems’, International Journal of Control, 82, 1070–1081) in which the authors study the problem of output feedback stabilisation for a class of Euler–Lagrange systems. The problem of global output feedback stabilisation of the practical system called the two-link manipulator system is solved. The output feedback scheme presented has better performance than the one exhibited in Ammar et al. (2009).

Keywords:

• nonlinear observer
• output feedback stabilisation
• global asymptotic stabilisation

Notes

Notes

1. Notice that this assumption can be omitted if the control u is bounded in norm which is meaningful from a practical point of view.

2. Notice that one can for instance simply take with c > 4.