Observability Analysis of Nonlinear Input-Linear Systems Based on Lie Derivations Using Interval Arithmetic

This paper presents a method to analyze the local observability of nonlinear systems with known inputs. For this purpose, an algorithm is presented that performs rank checking of the observability matrix using Lie derivatives. To overcome the limitations associated with inserting initial conditions and symbolically computing the derivatives, Interval arithmetic and Taylor series expansion with automatic differentiation are used. This allows observability to be analyzed over an entire domain. The algorithm provides the intervals for which observability cannot be proven by the rank criterion. This can be helpful when designing real-world applications. Two numerical systems are given as examples, with the first one having a constant input signal and the second one having an analytical input.