Distributed-Order Dynamic Systems

Zhuang Jiao is a PhD. candidate of Tsinghua University who worked for 12 months in the Center for Self-Organizing and Intelligent Systems (CSOIS) of Utah State University, directed by Dr YangQuan Chen. During his stay with CSOIS, he served as the Reference Library manager for the Applied Fractional Calculus Group at USU. He is the ever first derived the stability condition for DO LTIS. Professor Igor Podlubny is a Visiting Professor of CSOIS (Center for Self-Organizing and Intelligent Systems) of Utah State University doing collaborative research with Dr YangQuan Chen in various aspects of applied fractional calculus emphasizing research impacts to the community. Dr Podlubny is one of the leading researchers in the field of fractional calculus. His works are widely and heavily cited. Dr Podlubny serves as an Associate Editor for the flagship journal Fractional Calculus & Applied Analysis. See more at http://people.tuke.sk/igor.podlubny/ Dr. YangQuan Chen is currently an Associate Professor with tenure of electrical engineering at Utah State Univ. and the Director of the Center for Self-Organizing and Intelligent Systems with 30 plus members. Dr. Chen serves as an Associate Editor for Fractional Calculus & Applied Analysis, Fractional Differential Equations, ASME J. of Dynamic Systems, Measurement and Control, IEEE Transactions on Control Systems Technology, IFAC journal Mechatronics and ISA Transactions. He is also a Designated Editor for IFAC journal Control Engineering Practice. His main interests are in applied fractional calculus, systems and control, mechatronics, mobile actuator and sensor networks, UAV-based collaborative personal remote sensing. He has published with Springer two monographs (2010 and 2011) related to applied fractional calculus. We focus on the stability analysis of distributed-order linear time-invariant system, distributed-order signal processing and the numerical solution to discretization of distributed-order derivatives and integrals, and the numerical solution of ordinary and partial differential equations of distributed order. The proposed approach provide a general idea which can help researchers in science and engineering fields solve their issues.

• Introduction.- Distributed-order Linear Time-invariant System (DOLTIS) and Its Stability Analysis.- Noncommensurate Constant Orders as Special Cases of Doltis.- Distributed-order Filtering and Distributed-order Optimal Damping.- Numerical Solution of Differential Equations of Distributed Order.- Future Topics.- Appendix: MATLAB® Codes.

From the book reviews: "This book is a concise introduction to the theory and use of distributed-order systems. ... Written at the level of first- or second-year graduate student, the book is well suited as a self-contained introduction to an emerging area of research and applications." (IEEE Control Systems Magazine, October, 2013)