Design of Robust Lyapunov-Based Observers for Nonlinear Systems With Sum-of-Squares Programming

In this letter, we consider the problem of designing robust observers for uncertain polynomial systems. The results are applicable to polynomial systems with dynamics that are affine in the control and disturbance variables, and a perturbed linear output model. The input and disturbance variables can take values in convex and compact polytopes. We use sum-of-squares (SOS) methods to synthesize a Lyapunov-based robust state observer. In particular, given the dynamics of the observed system and the explicit robustness bounds, the polynomial dynamics of the observer and a worst-case convergence bound are obtained through the solution of an appropriately formulated SOS program. We also discuss an extension of the proposed class of robust observers that is applicable to the distributed state observation problem for uncertain networked polynomial systems.