Nonlinear filter design with integrator for a class of polynomial discrete-time systems

In this paper, we attempt to design a filter to estimate the state of polynomial discrete-time systems. In this work, a global filter design method for polynomial discrete-time systems by using SOS-SDP based is established without any assumptions about nonlinear terms of the error dynamics. In our work, to ensure a convex solution to the filter design problem can be obtained, an integrator is incorporated into the filter structure. This paper provides a potential solution to the filter design problem for polynomial discrete-time systems. Unfortunately, the price we pay is the computational burden due to a very large SDP size yields from the proposed method. The effectiveness of the proposed method is confirmed through a simulation example.