Robust H_infinity Filter Design for Lipschitz Nonlinear Systems via Multiobjective Optimization

In this paper, a new method ofH∞ observer design for Lipschitz nonlinear systems is proposed in the form of an LMI optimization problem. The proposed observer has guaranteed decay rate (exponential convergence) and is robust against unknown exogenous disturbance. In addition, thanks to the linearity of the proposed LMIs in the admissible Lipschitz constant, it can be maximized via LMI optimization. This adds an extra important feature to the observer, robustness against nonlinear uncertainty. Explicit bound on the tolerable nonlinear uncertainty is derived. The new LMI formulation also allows optimizations over the disturbance attenuation level (H∞ cost). Then, the admissible Lipschitz constant and the disturbance attenuation level of the H∞ filter are simultaneously optimized through LMI multiobjective optimization.