H∞ filtering and solution bound for nonlinear systems

In this paper, sufficient conditions are presented for the existence of a solution to the nonlinear H^∞ filtering problem. The conditions are expressed in terms of the solution to a Hamilton-Jacobi inequality involving only n+1 (for time-varying case) or n (for time-invariant case) independent variables. Both affine and general nonlinear systems are examined. In the time-invariant affine nonlinear case, we also present one kind of positive radial solution to the Hamilton-Jacobi inequality, and give an explicit estimation of the achievable disturbance attenuation level