Diversity and Non-integer Differentiation for System Dynamics

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.

• 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.