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

This paper presents the observer design to control and at the same time estimate the state of polynomial discrete-time systems. In general, to design observer for polynomial discrete-time system is difficult because the solution is nonconvex. More precisely, it is a nonconvex problem due to the relationship between the Lyapunov function and the observer gain is not jointly convex. Hence, it cannot be possible to be solved via semidefinite programming (SDP). In this work, to ensure a convex solution to the observer design problem can be obtained, an integrator is incorporated into the observer structure. By doing this, a convex solution can be guaranteed. The observer gains are then computed using SOS-SDP techniques.