Assoc. Prof. Mehmet Emir Koksal, Ondokuz Mayıs University, Turkey
Biograhy: Mehmet Emir Koksal is an Associate Professor of Mathematics at the Department of Mathematics of Ondokuz Mayıs University, Turkey. He received his PhD degree in Mathematics from the Gebze Institute of Technology in Turkey in 2009. After he received his PhD, he studied as a postdoctoral scholar at the Department of Mathematical Sciences of Florida Institute of Technology, Melbourne. His major field of study is development of numerical solution methods for PDEs using finite difference, element and volume methods. He has published a number of reviewed research papers on this field. He does also research on mathematical modeling and analyzing of various engineering problems using PDEs. His another research area is the study of existence and uniqueness of solutions of ODEs. Recently, he has started studying mainly on the investigation of commutativity of continuous and discrete time-varying linear systems. He works on the commutativity conditions of relaxed and unrelaxed linear time-varying systems, commutativity of feedback systems, decompositions of high-order systems, transitivity property of commutativity and benefits and applications of commutativity. His researches have been mainly supported by the Scientific and Technological Research Council of Turkey. On this field, he has led two national projects. He has published a number of reviewed research papers and received numerous grants and awards. He has served as a reviewer for over 50 refereed scientific journals and conferences and reviewed over 200 manuscripts. He has undertaken many administrative duties in various commission and committees of universities. Moreover, He has been a member of organizing and scientific committees of many famous international conferences.
Speech Title: On the Commutativity of Analog and Digital Systems
Abstract: Most control systems are composed of successive treatments of signals by a chain of subsystems. Each subsystem performs some part of a complete process. Most of the time, it is the designers' decision how and in what sequence the controllers are assembled with the plant when its control is of concern. The sequence of processing is important to achieve the desired aim with the maximum proficiency. The order of subsystems may be changed without affecting the overall functioning of the assembly so that an optimum sequence is achieved, but this is true if the subsystems interchanged are time invariant. If any one of the subsystems in the chain of process is of time varying, then this is not so easy since any arbitrary change will disturb the input-output relation of the whole system so that the main functioning disappears. In this case the problem of commutativity arises; that is, under what conditions the sequence of two subsystems can be changed so that the combined performance is invariant under this change. To arrive a better system performance, the sequence of two time-varying subsystems in a control system can be changed only if these subsystems are commutative. Otherwise, the complete system spoils its main functioning and the attempt becomes unsuccessful. In this talk, a panoramic review of these contributions will be introduced, and some new subjects are suggested for future research. The topics and/or the relevant important features that will be covered are listed as follows: Concept and definition of commutativity of systems, General commutativity conditions for relaxed and unrelaxed LTVASs, Commutativity of Euler systems, Commutativity of analog feedback systems, Decompositions of second and third-order LTVASs, Transitivity property, Benefits of commutativity, Discrete time systems, Future works.
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