Observability and detectability analysis of singular linear systems with unknown inputs

Abstract

Abstract-We study the observability problem of a general class of singular linear systems with unknown inputs. It is shown that, under some assumptions, the problem is equivalent to study the observability of a standard linear system with unknown inputs satisfying algebraic constraints. We obtain necessary and sufficient conditions for observability in terms of the zeros of the system matrix.Index Terms-Singular systems, strong observability, algebraic observability.

A divide-and-conquer approach to distributed attack identification

“…Additionally, a reconstruction of x 1 modulo V * 1 and x 2 modulo V * 2 can be obtained through standard algebraic techniques [10]. Finally, the presented lemmas extend the results in [18] by characterizing the subspaces of the state space that can be reconstructed with an algebraic method by processing the measurements y and their derivatives.…”

“…Our method builds upon the results presented in [18]. Consider the descriptor model (1) written in the semi-explicit form (see [1, Section IV.C])…”

Characterization of the minimum detectable fault of interval observers by using set-invariance theory

“…This two-tank system is a part of the well know four-tanks system benchmark proposed in [6]. Using the Euler discretization with a sampling time of 1s, the linearized model of this system can be written in the state-space form as in (1), where the state x indicates the water level of the tanks. The parameters of the model are • ω, υ and u denote the disturbance, the measurement noise and the input, respectively, which are considered unknown but bounded with the following offset magnitudes:…”

“…Due to unexpected existence of perturbations, disturbances and noises, estimating the fault value is quite difficult in a faulty system by using current FDI approaches [1], [8]. Therefore, the estimation of the magnitude of the fault, known as fault estimation, and its related approaches has been started to be researched, see e.g., [12], [17], [8] and the references therein.…”

A nonlinear Luenberger-like observer for nonlinear singular systems

“…Recently, Bejarano et al (2013) generalizes the observability for linear singular system to consider the unknown input case, by converting the singular system into a regular one with unknown inputs and algebraic constraints. Moreover, the assumption of regular matrix pencil for singular systems was removed as well in Bejarano et al (2011Bejarano et al ( , 2013. It has been extended in Bejarano et al (2012) and Bejarano et al (2015) to treat nonlinear singular systems.…”