Nonlinear observer design via convex optimization

This paper presents a nonlinear observer design technique based on Lyapunov´s second method which provides an observer gain matrix that stabilizes the error dynamics for a class of nonlinear systems. It is also shown how the observer gain matrix can be optimally chosen, via convex optimization, with respect to three different costs; specifically, the maximum singular value of the gain matrix, the decay rate of the error dynamics, and the H_∞ norm between disturbances and the estimation errors. Furthermore, the paper discusses how these different optimization criteria can be combined to provide Pareto optimal observer gain matrices. Simulation results for a representative problem is also given.