Preserving order observers for nonlinear systems

Preserving Order Observers provide an estimation that is always above or below the true variable and, in the absence of uncertainties/perturbations, the estimation converges asymptotically to the true value of the variable. In this paper we propose a novel methodology to design preserving order observers for a class of nonlinear systems in the nominal case or when perturbations/uncertainties are present. This objective is achieved by combining two important systemic properties: dissipativity and cooperativity. Dissipativity is used to guarantee the convergence of the estimation error dynamics, while cooperativity of the error dynamics assures the order preserving properties of the observer. The use of dissipativity for observer design offers a big flexibility in the class of nonlinearities that can be considered while keeping the design simple: it leads in many situations to the solution of a Linear Matrix Inequality (LMI). Cooperativity of the observer leads to a LMI. When both properties are considered simultaneously the design of the observer can be reduced, in most cases, to the solution of both a Bilinear Matrix Inequality (BMI) and a Linear Matrix Inequality (LMI). Since a couple of preserving order observers, one above and one below, provide an interval observer, the proposed methodology unifies several interval observers design methods. The design methodology has been validated experimentally in a three-tanks system, and it has also been tested numerically and compared to an example from the literature. Copyright c © 2012 John Wiley & Sons, Ltd.