Analysis of linear structured systems using a primal-dual algorithm

IFAC Proceedings Volumes

Hamelin

2008

To cite this version:Abstract: This paper deals with the state and input observability analysis for structured bilinear systems with unknown inputs. More precisely, we provide two groups of conditions, the first ones are necessary and the second ones are sufficient, to check whether or not a structured bilinear system generically state and input observable. These conditions, which are far to be trivial, are expressed in quite simple graphicterms. Moreover,the proposed method assumes only the knowledge of the system's structure and all the given conditions are easy to check because they deal with finding paths in a digraph. This makes the suggested approach particularly well suited to study large scale systems or systems with unknown parameters, as it may be the case during a conception stage.

Section: Resultsmentioning

confidence: 99%

State and input observability for structured bilinear systems: A graph-theoretic approach

IFAC Proceedings Volumes

Hamelin

2008

“…Furthermore, the algorithm used to check the sufficient condition is constituted by at most n(n + 1)/2 computations of function β. To compute such function, we use an algorithm which complexity order equals O(N 3 × M 0.5 ) (Boukhobza et al, 2007;Martinez-Martinez et al, 2006) using the primal-dual algorithm (Hovelaque et al, 1996).…”

Section: Resultsmentioning

confidence: 99%

Generic uniform observability analysis for bilinear systems

2008

Automatica

In this paper, we study the property of generic uniform observability for structured bilinear systems. More precisely, to check whether or not a structured bilinear system generically uniformly observable, we provide a group of necessary conditions and second group of sufficient ones. These conditions are expressed in quite simple graphic-terms. On the one hand, all the given conditions are easy to check because they deal with finding paths in a digraph. On the other hand, the proposed method is based on a graph-theoretic approach and assumes only the knowledge of the system's structure. This makes the suggested approach particularly well suited to study large scale systems or systems with unknown parameters, as it may be the case during a conception stage.

“…The computation of a maximal size linking has a complexity order equal to O(W 2 ·M 0.5 ) using a transformation of a digraph into a flow graph (Martinez-Martinez et al [2006]), where M = (n + q)(n + q) + (n + q)p is the maximal number of edges and W = n + p + q is the number of vertices in the digraph. The computation of function µ is done using the primaldual algorithm (Hovelaque et al [1996]). Next, the computation of β 1 is equivalent to the computation of a maximal matching in a bipartite graph.…”

Section: Resultsmentioning

confidence: 99%

Observability analysis for networked control systems: a graph theoretic approach

IFAC Proceedings Volumes

Hamelin

2008

To cite this version:Abstract: This paper deals with the state and input observability analysis for Networked Control Systems which are composed of interconnected subsystems that exchange data through communication networks. The proposed method is based on a graph-theoretic approach and assumes only the knowledge of the system's structure. More precisely, for the so-called distributed decentralized and distributed autonomous observation schemes, we express, in simple graphic terms, necessary and sufficient conditions to check whether or not a considered subsystem is strongly observable. These conditions, which allows also to characterize all the strongly observable state and input components of each subsystem, are easy to check because they are based on comparison of integers and on finding paths in a digraph. This makes our approach suited to study large scale distributed systems.