The bounded Jacobian approach to nonlinear observer design

This paper presents a new observer design technique for a nonlinear system with a globally (or locally) bounded Jacobian. The approach utilized is to use the mean value theorem to express the nonlinear error dynamics as a convex combination of known matrices with time varying coefficients. The observer gains are then obtained by solving linear matrix inequalities (LMIs). The developed approach can enable observer design for a large class of differentiable nonlinear systems. Its advantage is that it enables easy observer design for a much wider range of operating conditions compared to linear or Lipschitz observer design methods. The use of the observer design technique is illustrated for estimation of vehicle roll angle in an automotive system involving a complex nonlinearity. The performance of the new observer is shown to be clearly superior to that of a standard Lipschitz observer.