LMI conditions for designing rational nonlinear observers with ℋ∞ performance

This paper presents a technique for designing rational nonlinear observers for rational nonlinear systems with ℋ∞ performance. The approach is based on a Lyapunov function that is rational on the estimation error and on the system states. The design conditions are formulated as Linear Matrix Inequalities (LMIs). If the conditions are satisfied, then the estimation error is guaranteed to asymptotically converge to zero for initial conditions on an estimated region of attraction. An optimization procedure for enlarging the region of attraction is also provided and an example is used to illustrate the results.