Nonlinear observer design using Lyapunov functions and SOS techniques

In this paper an observer for a polynomial nonlinear (nonautonomous) system constrained to a bounded subset of the state space is considered. The presented approach allows the construction of a locally asymptotically stable observer, which is guaranteed to be stable for any possible state within the limits. It is based on a theorem of Jacobi and Prestel. The problem is rewritten as an optimization problem using sum of squares (SOS) polynomials. The coefficients of these polynomials are interpreted as decision variables which form the basis of a convex optimization problem with linear matrix inequalities (LMIs). It can be easily implemented and solved with available software. The applicability of our approach is shown for an example.