Routh-type Table Test for Zero Distribution of Polynomials with Commensurate Fractional and Integer Degrees to Dynamic Systems Stability and Performance Analysis and Design

Prof. Sheng-Guo Wang
University of North Carolina – Charlotte, USA


时 间:7月11日下午2:00-3:00;

地 点:张江校区微电子楼269会议室

This speech presents our novel Routh-type table test methods for zero distribution of polynomials with commensurate fractional degrees (PCFDs) in the left-half plane, right-half plane and imaginary axis of the complex plane as the first time in the literature.
It is well known that it is impossible to have a closed form of algebraic expression for the zeros of general polynomials with integer degree higher than four, not to mention fractional degree polynomials. Thus, any zero solving method and algorithm for general polynomials are some approximation ways in theoretical and essential sense. On the other hand, the classical Routh table test is theoretical correct and accurate for zero distribution analysis of polynomials with integer degrees, and has been widely used to analyze dynamic systems stability described by their integer degree differential equations.
Thus, what is the Routh-type table test for zero distribution of PCFDs for systems described by fractional order differential equations, which is theoretically and essentially accurate? This seminar is to present the solution. Furthermore, the singular cases of the presented methods are discussed and handled efficiently. Necessary and sufficient conditions for the second singular case are completely analyzed in terms of symmetric zeros. The dynamic system stability and performance analysis and design by the proposed new table test is presented.
All presented new methods and results are strictly and theoretically proved. Numerical examples, including new emerging fractional order circuit system analysis and design example, further illustrate the correctness and effectiveness of the presented methods.
Moreover, the Routh-type test is a necessary and sufficient condition for stability test with the simplest arithmetic calculations in both theoretical and essential senses. The presented methods can have various potential applications to broad areas, especially for various systems described by fractional order differential equations.

Bio of Prof. Sheng-Guo Wang:
Prof. Sheng-Guo Wang is a tenured full professor at the University of North Carolina at Charlotte (UNC Charlotte), USA. He received his B.S. and M.S. in electrical engineering from University of Science and Technology of China in 1967 and 1981 respectively, and PhD in electrical and computer engineering from University of Houston in 1994.
He has been the PI for numerous research projects since 1974. Prof. Wang is a recipient of China National Science Conference Award 1978, one of the highest academic honors in China, and US Fulbright Senior Scholar Award of 2016-2017, and many other academic awards, e.g., his recent NCDOT research project, titled “Improvements to NCDOT’s Wetland Prediction Model” (4-30-2012 ~ 8-15-2014), has won a US national 2015 “Sweet 16” High Value Research Award recognized by AASHTO (American Association of State Highway and Transportation Officials) and RAC (Research Advisory Committee) in 2015, and also acknowledged at 2016 TRB (Transportation Research Board) Annual Meeting, National Academies of Sciences-Engineering-Medicine in 2016.


Some Basic Topic and Discussion on Machine Learning – SVM
Prof. Sheng-Guo Wang

This seminar is for some basic topic and discussion on machine learning methods and their features. The focus is on the basic principle and its mathematics as well as its applications of SVM (support vector machine) and kernel machine for classification and regression.



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