LMI Conditions for Designing Rational Nonlinear Observers with Guaranteed Cost

This paper presents a technique for designing rational nonlinear observers for rational nonlinear systems with guaranteed cost performance. The approach is based on a Lyapunov function that is quadratic in the estimation error and rational in 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. An example is used to illustrate the results.