A comprehensive introduction to the geometric theory of linearmultivariable systems

A simple tutorial introduction to the geometric theory of linear multivariable control is presented. This corresponds to approximately three two-hour lectures in a graduate-level course. The authors emphasise the intuitive control interpretation of the main geometric concepts. To this end, the authors focus interest on trajectory formulation for subspace invariance and discrete-time interpretation of the basic subspaces and their construction algorithms. Application of geometric theory for solving the disturbance decoupling problem is illustrated via two pedagogical examples     

Zero Orders and Dimensions of Some Invariant Subspaces in Linear Structured Systems

In this paper we consider linear structured systems which represent a large class of parameter-dependent linear systems and we study invariants for such systems under a large group of transformations including state feedback. In this context we consider the dimension of the maximal output-nulling invariant subspace of a linear structured system, the number and structure of its invariant zeros and its structure at infinity. We give generic characterizations of the invariants in terms of properties of the directed graph that can be naturally associated with a linear structured system. Date received: March 1, 2002. Date revised: April 1, 2003. The first authors stay at the Laboratoire dAutomatique de Grenoble was supported by grants of the Netherlands Organization for Scientific Research (NWO), the Institut National Polytechnique de Grenoble (INPG) and the French Ministry of Research.     

Input addition and leader selection for the controllability of graph-based systems

In this paper, we consider dynamical graph-based models, which are well fitted for the structural analysis of complex systems. A significant amount of work has been devoted to the controllability of such graph based models, e.g. recently for multi-agent systems or complex networks. We study here the controllability through input addition in this framework. We present several variants of this problem depending on the freedom which is left to the designer on the additional inputs. We use a unified framework, which allows us to encompass the different applications and representations (large scale systems, complex communications networks, multi-agent systems, …) and provide convenient graph tools for their analysis. Our contribution is to characterize the structural modifications of the system resulting from an input addition (or a leader selection) and of the mechanisms which lead to controllability. We provide information on the possible location of additional inputs and on the minimal number of inputs to be added for controllability.     

Feedback stabilization of some event graph models

The authors introduce several notions of stability for event graph models, timed or not. The stability is similar to the boundedness notion for Petri nets. The event graph models can be controlled by an output feedback which takes information from some observable transitions and can disable some controllable transitions. The controller itself is composed of an event graph. In this framework the authors solve the corresponding stabilization problems, i.e., they wonder if such a controller may prevent the explosion of the number of tokens     

Further comments on "Aggregation matrix for the reduced-order continued fraction expansion model of Chen and Shieh"

Abstract-Contrary to what has been proposed in a recent paper, a reduced model by a continued fraction expamion method is not generally an aggregated model we observe in the example given by the authors themselves that the aggregation relationship is not valid.     

Optimal choice of modes for aggregation

In this note a method of system simplification by aggregation is proposed. This method is based on the hypothesis of non-observability of conserved modes on the output error. It leads to a simple combinatorial algorithm of optimization.     

On the disturbed fault detection and isolation problem

In this paper we study the fault detection and isolation problem in presence of disturbances. In the case of observer-based residual generation, the problem amounts to finding two gain matrices such that two problems are simultaneously solved. These problems are insensitivity of the residuals to disturbances and the existence of some special structure for the transfer from faults to residuals. We prove in this paper that this joint problem can be solved if and only if the usual (undisturbed) fault detection and isolation problem can be solved for a system with a reduced number of outputs.     

Structured time-delay systems: A graph approach

In this paper, linear structured systems with delays are defined and a simple graph representation for these systems is given. Then, the generic controllability of time-delay systems is introduced and a graph criterion for controllability is provided. The generic row-by-row decoupling problem without prediction of such systems is then studied and graphical necessary and sufficient solvability conditions for this problem is derived.