Interpolatory methods for model reduction (Q6595954)

In a number of fields, the dynamical system describing the phenomena to be predicted or controlled has a very huge size (e.g. several hundred thousands states). Examples of those fields are: image reconstruction in diffuse optical tomography, indoor environments, commercial aircraft design and certification (and this reviewer would add: the interconnected electric network in Western Europe or North America). Obtaining a reduced order model, still accurate, is a very important issue and often a first step for rapid prediction or control design. Several well tested methods for model reduction are existing and one of them, based on interpolations of several kinds, is the subject of the book. It is intended to readers (students, researchers and practitioners) who have an advanced undergraduate or early graduate level in control theory and/or engineering.\N\NThe book is divided into four parts: the 1st one contains preliminaries, including some background (that not all experts in control theory have), the 2nd one presents the core concepts in the case of linear time-invariant systems, the 3rd one considers the case of parameter-dependent or nonlinear systems, and the last part is about advanced topics. Generally speaking, the model reduction is based either on state-space system data or on input-output data. In addition to the theory (reduced to the minimum, for the reader's convenience and to limit the length of the book), the book contains many examples which illustrate the efficiency of the methods presented. A list of 318 references is provided, and the pages where each reference is used are indicated. The subject index could have been more detailed.\N\NAs said in the Preface, ``this book is the first reference work to give comprehensive coverage of interpolatory methods for model reduction''. The authors did an excellent job and the book will be very useful for people faced with the problem of model reduction.