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Publisher’s description: This book aims at reviewing recent progress in the direction of algebraic and symbolic computation methods for functional systems, e.g. ODE systems, differential time-delay equations, difference equations and integro-differential equations. In the nineties, modern algebraic theories were introduced in mathematical systems theory and in control theory. Combined with real algebraic geometry, which was previously introduced in control theory, the past years have seen a flourishing development of algebraic methods in control theory. One of the strengths of algebraic methods lies in their close connections to computations. The use of the above-mentioned algebraic theories in control theory has been an important source of motivation to develop effective versions of these theories (when possible). With the development of computer algebra and computer algebra systems, symbolic methods for control theory have been developed over the past years. The goal of this book is to propose a partial state of the art in this direction. To make recent results more easily accessible to a large audience, the chapters include materials which survey the main mathematical methods and results and which are illustrated with explicit examples.
The articles of this volume will be reviewed individually.
Indexed articles:
Cluzeau, Thomas; Koutschan, Christoph; Quadrat, Alban; Tõnso, Maris, Effective algebraic analysis approach to linear systems over Ore algebras, 3-52 [Zbl 1453.93042]
Cluzeau, Thomas; Quadrat, Alban, Equivalences of linear functional systems, 53-86 [Zbl 1448.93053]
Quadrat, Alban; Regensburger, Georg, Computing polynomial solutions and annihilators of integro-differential operators with polynomial coefficients, 87-114 [Zbl 1540.47112]
Lange-Hegermann, Markus; Robertz, Daniel, Thomas decomposition and nonlinear control systems, 117-146 [Zbl 1451.93171]
Diop, Sette, Some control observation problems and their differential algebraic partial solutions, 147-160 [Zbl 1466.93028]
Boulier, François; Lemaire, François; Rosenkranz, Markus; Ushirobira, Rosane; Verdière, Nathalie, On symbolic approaches to integro-differential equations, 161-182 [Zbl 1467.93146]
Ushirobira, Rosane; Korporal, Anja; Perruquetti, Wilfrid, Algebraic estimation in partial derivatives systems: parameters and differentiation problems, 183-200 [Zbl 1448.65021]
Bouzidi, Yacine; Rouillier, Fabrice, Symbolic methods for solving algebraic systems of equations and applications for testing the structural stability, 203-237 [Zbl 1448.93052]
Boussaada, Islam; Niculescu, Silviu-Iulian, A review on multiple purely imaginary spectral values of time-delay systems, 239-258 [Zbl 1444.93019]
Schilli, Christian; Zerz, Eva; Levandovskyy, Viktor, Controlled and conditioned invariance for polynomial and rational feedback systems, 259-293 [Zbl 1451.93127]
Pereira, Ricardo; Rocha, Paula, A note on controlled invariance for behavioral nD systems, 295-306 [Zbl 1442.93011]