Robust observer design for Lipschitz nonlinear systems using quadratic polynomial constraints

This paper discusses the observer design for the uncertain Lipschitz nonlinear systems. A new stability analysis method for the Lure problem is first presented. Then, a nonlinear observer is proposed so that the observer error dynamic model can be transformed to an equivalent Lure system in which the input-output relationship of the nonlinear memoryless block is belong to the semi-algebraic set defined by several quadratic polynomial constraints. A sufficient condition for the exponential stability of the observer error dynamics is formulated in terms of the feasibility of linear matrix inequalities (LMIs).