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We consider here the fault detection and isolation (FDI) problem for linear systems. We are interested in designing a set of observer-based residuals, in such a way that the transfer from the faults to the residuals is diagonal and the transfer from the disturbances to the residuals is zero. We deal with this problem when the system under consideration is structured, that is, the entries of the system matrices are either fixed zeros or free parameters. This problem can be solved in terms of the graph that can be associated in a natural way with a structured system. When the FDI solvability conditions are not satisfied, we assume that internal variables can be measured at a cost and look into the question of wether the problem is solvable with these new measurements. We give solvability conditions for a solution with a minimal number of additional sensors and among such solutions provide a minimal cost solution for the sensor location problem under consideration. We pay particular attention to the internal analysis of the system, and we propose a structural decomposition of the system associated graph based on some particular separators. This analysis leads to the definition of a reduced system. We prove that some potential additional sensors are inefficient for solving our FDI problem and that the FDI problem can be solved using only measurements on the reduced system

Fault detection and isolation (FDI) problems are here consid- ered for linear systems with faults and disturbances. We design a set of ob- server-based residuals in such a way that the transfer from the disturbances to the residuals is zero, and the transfer from the faults to the residuals al- lows fault isolation. We are interested in obtaining a transfer function from faults to residuals with either a diagonal structure (i.e., a dedicated struc- tured residuals set) or a triangular one. We deal with this problem when the system under consideration is structured. That is, the entries of the system matrices are either fixed zeros or free parameters. To a structured system, one can associate in a natural way a directed graph. We can then provide necessary and sufficient conditions under which the FDI problems have a solution for almost any value of the free parameters. These conditions are simply expressed in terms of input-output paths in the associated graph. Index Terms—Fault detection and isolation, graph theory, model-based approach, structured residuals, structured systems.

In this paper, structured systems described by state-space models are considered. For these systems, the entries of the state-space model matrices are assumed to be either fixed zeros or free independent parameters. We study the dynamic decoupling of structured linear systems. It turns out that a large class of systems which is not state feedback decouplable can be made decouplable by the addition of a simple structured precompensator. Such a precompensator then has the property to be independent of the system parameters. We give a necessary and sufficient condition for a structured system to be made feedback decouplable using a parameter independent precompensator. Furthermore, we prove that when such a solution exists, the precompensator can be chosen to be diagonal. In this case the precompensator is constructed via a simple combinatorial algorithm. Our approach is based on a graph representation of the structured system. All the results of this paper are related to some particular shortest sets of input-output paths in the graph associated with the structured system.

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.

The feedback decoupling of structured linear systems is considered. Using results gathered on decoupling and the graph characterization of the structure at infinity, a necessary and sufficient decoupling condition for structured systems is developed. This condition has a graphical interpretation in terms of shortest input-output paths. >

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. >

The disturbance rejection problem for structured systems is solved. A graph is associated with such a structured system. It turns out that disturbance rejection is solvable by state feedback whenever the control inputs reach the outputs more quickly than the disturbances in the associated graph. The infinite structure of a structural system is characterized in terms of input-output paths in the associated graph. Then, as a consequence, the disturbance rejection problem is solved. >

The dynamic state feedback block decoupling problem in the general case, i.e. with singular or nonsingular input transformations, is solved. It is proven that the problem is solvable if the number of inputs is large enough. The main tools for this study are some invariant spaces associated with the columns infinite behavior of a rational matrix. It turns out that when the problem is solvable, it is also solvable with stability. >

The infinite zero structure of linear multivariable systems is investigated via the geometric approach. The basic tools used are the new concepts of almost (A, B)-invariant and almost controllability subspaces. These concepts permit advantageous geometric interpretation of infinite zeros. This interpretation is a natural generalization of the finite case. Connection is made with the Smith McMillan structure at infinity of the transfer matrix. Structural properties of irreducible systems are investigated leading to a generalization of Morse theorem on prime systems.

This paper describes the practical education that is given at the Grenoble Polytechnic Institute in the recently created section of control engineering. A set of laboratories in the main areas of the curriculum is briefly presented: control of continuous systems, logic, microprocessors and real-time systems, and signal processing. Specific emphasis is placed upon the fact that this mode of teaching is complete in itself, and that the interrelationship of different experiments becomes more and more important as the academic session progresses. The practical education is supplemented by a three-month period in industry where students are generally given good opportunities for synthesizing the various facets of their technical knowledge.

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.