ODE observers for DAE systems

Abstract

We consider linear time-invariant differential-algebraic systems which are not necessarily regular. The following question is addressed: when does an (asymptotic) observer which is realized by an ordinary differential equation (ODE) system exist? In our main result we characterize the existence of such observers by means of a simple criterion on the system matrices. To be specific, we show that an ODE observer exists if, and only if, the completely controllable part of the system is impulse observable. Extending the observer design from earlier works we provide a procedure for the construction of (asymptotic) ODE observers.

Partial impulse observability of linear descriptor systems

“…1]. Likewise, again invoking ker E ∩ ker C ⊆ W * [E,A,0,C] , the characterizations (iv) and (v) in Theorem 3.7, for the case K = I, imply alternative characterizations for causality of system (1.1), which can be found in [5,21].…”

“…Nowadays, there are several equivalent characterizations for the full-state estimation of systems (1.1), and algorithms for the construction of the estimators exist. A relatively complete literature for the theory of full-state estimation of LTI descriptor systems (1.1) can be found in [4,5,17,21] and the references therein. On the other hand, the problem of functional (or partial-state) estimation has been first addressed in the pioneering work of Dai [9] and Minamide et al [27] on regular descriptor systems.…”

Observers for differential-algebraic systems with Lipschitz or monotone nonlinearities

“…[25]. In the present paper we allow the function f = f L f M to be a combination of a function f L satisfying (7) and a function f M satisfying (8). Therefore the presented theorems cover a larger class of systems.…”

“…We stress that such an observer candidate is a DAE system in general; for the investigation of the existence of ODE observers see e.g. [5,8,19]. This paper is organised as follows: We briefly state the basic definitions and some preliminaries on matrix pencils in Section 2.…”

Partial detectability and generalized functional observer design for linear descriptor systems

“…Exploiting the behavior B, various observability and detectability concepts for descriptor systems (1) are studied in [7]. Existence conditions for full state and functional observers of descriptor systems have been investigated in [8]- [14], see also the references therein. Throughout the article, we assume that the behavior B is nonempty, which amounts to the existence of an admissible pair for (1), consisting of an admissible initial condition and input function, see also [9].…”