  This article approaches deterministic filtering via an application of the
min-plus linearity of the corresponding dynamic programming operator. This
filter design method yields a set-valued state estimator for discrete-time
nonlinear systems (nonlinear dynamics and output functions). The energy bounds
in the process and the measurement disturbances are modeled using a sum
quadratic constraint. The filtering problem is recast into an optimal control
problem in the form of a Hamilton-Jacobi-Bellman (HJB) equation, the solution
to which is obtained by employing the min-plus linearity property of the
dynamic programming operator. This approach enables the solution to the HJB
equation and the design of the filter without recourse to linearization of the
system dynamics/ output equation.
