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The Disturbance Rejection by Measurement Feedback (DRMF) is a well known problem mixing control and estimation aspect, whose resolution relies on a good knowledge of the system structural properties. The solvability conditions are highly dependent on the sensor locations. In this paper we analyze the sensor location issues for the DRMF of structured systems which are a large class of parameter dependent linear systems. The sensor location for this problem is already solved in the literature for the case of systems with a single disturbance. It turns out that the sensors must measure state variables in regions close enough to the action of the disturbance. In the multiple disturbance case, the problem is much more complex; some close measurements may be useless while others more distant are useful. In this paper we solve the multiple disturbance case and provide with a full characterization of the sensor location for DRMF. Sets of state variables that are not useful to measure because they never belong to a minimal sensor solution as well as sets of state variables that belong to minimal solutions are determined easily on the system associated graph. [ABSTRACT FROM AUTHOR]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: In this paper a new necessary and sufficient condition is proposed for the solvability of the Disturbance Rejection by Measurement Feedback (DRMF) problem involving linear structured systems. The associated system graph can be used to easily check whether or not the condition holds. In relation to the DRMF problem, two issues related to the available sensor set have been investigated: [-] Sensor number and location: when the DRMF problem is not solvable with the given sensor set, how many sensors are needed and where should they be located to make the DRMF problem solvable? [-] Sensor classification: when the DRMF problem is solvable with the given sensor set, what is the impact of the failure of a sensor on the solvability? Based on the new condition, a lower bound can be determined for the number of sensors required. Moreover, measuring state variables outside a given subset is found to be of no use. To solve the DRMF problem, it is sufficient to measure state variables sufficiently close to the disturbances in the associated system graph. Sensor classification is used to distinguish between essential sensors, i.e. sensors for which failure leads to unsolvability, and useless sensors that have no impact on solvability. Partial classification results are provided for the general case and a complete characterization of essential and useless sensors is provided for the single disturbance case. [Copyright &y& Elsevier]

Abstract: In this paper we tackle the sensor location problem for fault detection and isolation based on structural analysis for linear systems with faults. 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. With such structured systems one can associate a graph. A dedicated residual set is designed using a bank of observers for solving the problem. A major tool in this analysis is the notion of input separator in the associated graph, these separators form a lattice structure. The main contribution of this paper is the formulation of necessary and sufficient solvability conditions for the problem in terms of number of additional sensors measuring variables between faults and input separators in the associated graph. [Copyright &y& Elsevier]

In this survey paper, we consider linear structured systems in state space form, where a linear system is structured when each entry of its matrices, like A,B,C and D, is either a fixed zero or a free parameter. The location of the fixed zeros in these matrices constitutes the structure of the system. Indeed a lot of man-made physical systems which admit a linear model are structured. A structured system is representative of a class of linear systems in the usual sense. It is of interest to investigate properties of structured systems which are true for almost any value of the free parameters, therefore also called generic properties. Interestingly, a lot of classical properties of linear systems can be studied in terms of genericity. Moreover, these generic properties can, in general, be checked by means of directed graphs that can be associated to a structured system in a natural way. We review here a number of results concerning generic properties of structured systems expressed in graph theoretic terms. By properties we mean here system-specific properties like controllability, the finite and infinite zero structure, and so on, as well as, solvability issues of certain classical control problems like disturbance rejection, input–output decoupling, and so on. In this paper, we do not try to be exhaustive but instead, by a selection of results, we would like to motivate the reader to appreciate what we consider as a wonderful modelling and analysis tool. We emphasize the fact that this modelling technique allows us to get a number of important results based on poor information on the system only. Moreover, the graph theoretic conditions are intuitive and are easy to check by hand for small systems and by means of well-known polynomially bounded combinatorial techniques for larger systems. [Copyright &y& Elsevier]

This paper focuses on the problem of uniform asymptotic stability of a class of linear neutral systems. Sufficient conditions for delay-dependent stability are given in terms of the existence of solutions of some linear matrix inequalities. Furthermore, the proposed technique extends to neutral systems the results obtained for delay-difference equations using model transformations. Illustrative examples are included. [Copyright &y& Elsevier]