An approach to determine observability of nonlinear systems using interval analysis

This paper provides an iterative interval-based algorithm which determines whether a nonlinear system is observable on a given hyperrectangle. Many applications work with a finite set of the possible state space. In case the nonlinear system is not entirely observable on a given state space the local observability is provided by the algorithm. The necessary observability matrix is calculated through computing Lie derivatives directly by using power series. The nonlinear system is examined to that effect that the states are distinguishable for an observer. The indistinguishable sets are checked whether the observability matrix is full rank. Finally, the capability of the introduced algorithm is illustrated by means of two examples.