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Diversity and Non-integer Differentiation for System Dynamics

Alain Oustaloup, Institut Polytechnique de Bordeaux, Enseirb-Matmeca, France

ISBN: 9781848214750

Publication Date: July 2014   Hardback   384 pp.

160.00 USD

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Based on a diversity-structured approach which is notably inspired by various natural forms of diversity (biological among others), this book unquestionably offers a framework, on the one hand, to the introduction of non-integer differentiation (otherwise known as fractional differentiation) as a modeling tool and, on the other hand, to the use of such a modeling form to highlight dynamic performances (and notably of damping) unsuspected in an “integer” approach of mechanics and automatic control. The “non-integer” approach indeed enables us to overcome the mass-damping dilemma in mechanics and, consequently, the stability-precision dilemma in automatic control.
This book has been written so that it can be read on two different levels: the first chapter achieves a first level of presentation which goes through the main results while limiting their mathematical development; the five remaining chapters constitute a second level of presentation in which the theoretical passages, deliberately avoided in the first chapter, are then developed at the mathematical level, but with the same goal of simplicity which aspires to make this book an example of pedagogy.


1. From Diversity to Unexpected Dynamic Performances.
2. Damping Robustness.
3. Non-Integer Differentiation, its Memory and its Synthesis.
4. On the CRONE Suspension.
5. On the CRONE Control.
6. Recursivity and Non-Integer Differentiation.
Appendix 1. Damping of a Usual Automotive Suspension.
Appendix 2. Relaxation of Water on a Porous Dyke.
Appendix 3. Systems with Explicit and Implicit Generalized Derivative.
Appendix 4. Generalized Differential Equation and Generalized Characteristic Equation.
Appendix 5. CRONE Control Response with Initial Conditions.
Appendix 6. Fractality and Non-integer Differentiation.

About the Authors

Alain Oustaloup is Professor in automatic control at the Institut Polytechnique de Bordeaux, Enseirb-Matmeca, France. His research works focus on non-integer differentiation and its applications in engineering sciences. In the 1980s, he developed a realistic synthesis method of non-integer differentiation. This method, which is at the origin of several applications of non-integer differentiation, has enabled him to invent both the CRONE control and the CRONE suspension.


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