Book review: 'Linear Systems Theory: A Structural Decomposition Approach', B.M. Chen, Z. Lin, Y. Shamash, Birkhauser, Boston, 2004, 415pp, ISBN 0-8176-3779-6

The structural and geometric approach is a consolidated means of analysis and synthesis in multivariable linear systems. Introduced in the late 1960s, this approach has received a multiplicity of contributions throughout the following decades, thus giving rise to a complete theory, expounded in the authoritative books [Wonham 1985] and [Basile and Marro 1992]. The fundamental objects of this theory (e.g. controlled invariant subspaces, controllability subspaces, conditioned invariant subspaces, etc.) are also extensively treated in recent books for graduate level courses in system theory, like e.g. [Rugh 1996] and [Trentelman, Stoorvogel and Hautus 2001]. Nonetheless, the research domain of system structure and control is still very active (see e.g. [Malabre, Plenary lecture, 2nd IFAC Symposium on System, Structure and Control, Mexico, 2004] and the references cited therein). In fact, now that the ever increasing complexity of control systems shows as the most challenging research fields those concerning robustness, nonlinear systems, failure detection and fault tolerance, hybrid systems etc, the interest for the structural aspects of systems which are assumed to be exactly described by linear models, is still motivated by several reasons...