Observer design for nonlinear systems: stability and convergence

This paper presents an observer design methodology for a class of nonlinear systems in which the nonlinearity is assumed to be Lipschitz. The stability of the observer is shown to be related to finding solutions to a Riccati inequality. Via a co-ordinate transformation, the Riccati inequality is reformulated as a Linear Matrix Inequality amenable to convex optimization. The result is a systematic algorithm that finds a stable observer whenever the Riccati inequality has a feasible solution. Other attractions of the method lie in the fact that the value of the maximum allowable Lipschitz constant for stability can be calculated and that the desired convergence rate can be incorporated into the design procedure.