Linear H∞ filter design for a class of uncertain nonlinear systems

This paper deals with the linear H_∞ filtering problem for a class of regionally stable uncertain nonlinear systems subject to bounded disturbances and measurement noises. The nonlinear systems is represented by differential-algebraic equations where the system matrices are allowed to be rational functions of the state and uncertain parameters. For this class of systems, LMI conditions are proposed for ensuring a prescribed upper-bound on the L₂-gain of the input-to-estimation error operator for a given linear asymptotically stable filter. The result is based on polynomial Lyapunov functions. Then, using an appropriate parameterization of the Lyapunov function we extend the analysis result for designing linear filters in a H_∞ sense via a convex optimization problem.