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Generic properties and control of linear structured systems: A survey. (English) Zbl 1023.93002

The authors have written an interesting survey on generic properties of structured systems. The system model considered is the state-space model of linear time-invariant systems denoted by \((A,B,C,D)\). In a structured system only the structure of the above matrices is known, that is, the zero pattern of the entries. Thus, from the directed graphs of the matrices one can study different properties that only depend on the structure (pattern) of the system. With this combinatorial technique the authors survey results on controllability, the characterization of the generic structure at infinity, the position and the orders of the finite zeros. Further, the generic solvability conditions of the state feedback decoupling and the state feedback disturbance rejection are characterized. The last two problems considered in the paper are the decentralized control problem and the fault detection and isolation problem.
In spite of this paper being a well-written survey, the authors point out that the objective of it is not to be exhaustive but to convince the reader of the interest of the generic approach, which is explained in section 3. I am sure that the authors will reach their objective of keeping some readers working on some open problems pointed out at the end of the survey.

MSC:

93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory
93C05 Linear systems in control theory
05C90 Applications of graph theory

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