Nonlinear observer design with robustness of transient behavior: Application to a flexible-joint robot

Asymptotic stability is a minimum requirement to be met in control and observation exercises. Quantification and control of the transient behavior is generally stated as non-convex optimization problem which involves additive penalty to asymptotic stability. In this paper, a convex-optimization approach to nonlinear observer design with robustness of transient behaviors is presented. It is shown that the overall performances of the observer estimates are attached to the solution of linear matrix inequalities. Numerical simulations are given to validate the theoretical results.