Nonlinear Unknown Input Observability: Extension of the Observability Rank Condition

Nonlinear Unknown Input Observability: Extension of the Observability Rank Condition and the Case of a Single Unknown Input

This paper investigates the unknown input observability problem in the nonlinear case under the assumption that the unknown inputs are differentiable functions of time (up to a given order). The goal is not to design new observers but to provide simple analytic conditions in order to check the weak local observability of the state. The analysis starts by extending the observability rank conditi...

Observability of Nonlinear Input-Affine Systems

The main aim of this paper is to characterize the set of states indistinguishable from a given state of a general nonlinear input-affine control system with complete and smooth vector fields and smooth output functions. For this purpose, we introduce the extended observation space, and show that the set of states indistinguishable from a given state is the intersection of level sets containing ...

Nonlinear Unknown Input Observability: Analytical expression of the observable codistribution in the case of a single unknown input

Observability of Nonlinear Systems

Abstract. Observability of a general nonlinear system—given in terms of an ODE ẋ = f(x) and an output map y = c(x)—is defined as in linear system theory (i.e. if f(x) = Ax and c(x) = Cx). In contrast to standard treatment of the subject we present a criterion for observability which is not a generalization of a known linear test. It is obtained by evaluation of “approximate first integrals”. Th...

Observability and Forward-Backward Observability of Discrete-Time Nonlinear Systems

In this paper, we study the observability properties of nonlinear discrete time systems. Two types of contributions are given. First, we present observability criteria in terms of appropriate codistributions. For particular, but significant, classes of systems we provide criteria that require only a finite number of computations. Then, we consider invertible systems (which includes discrete-tim...