EE Seminar: Revisiting Totally Positive Differential Systems: A Tutorial and New Results

10 ביוני 2018, 15:00 
חדר 011, בניין כיתות-חשמל 

(The talk will be given in English)

 

Speaker:     Prof. Michael Margaliot
                   Department of Electrical Engineering Systems, Tel Aviv University

 

Sunday, June 10th, 2018
15:00 - 16:00

Room 011, Kitot Bldg., Faculty of Engineering

 

Revisiting Totally Positive Differential Systems: A Tutorial and New Results

 

Abstract

 

A matrix is called totally nonnegative (TN) if all its minors are nonnegative, and totally positive (TP) if all its minors are positive. Multiplying a vector by a TN matrix does not increase the number of sign variations in the vector. In a largely forgotten paper, Schwarz (1970) considered matrices whose exponentials are TN or TP. He also analyzed the evolution of the number of sign changes in the vector solutions of the corresponding linear system. 

 

In a seemingly different line of research,  Smillie (1984), Smith (1991), and others analyzed the stability of nonlinear tridiagonal cooperative systems by using the number of sign variations in the derivative vector as an integer-valued Lyapunov function.

 

We provide a tutorial on these fascinating research topics and show that they are intimately related. This allows to derive generalizations of the results by Smillie (1984) and Smith (1991) while simplifying the proofs.  This also opens the door to many new and interesting research directions.

 

Joint work with and Eduardo D. Sontag, Northeastern University.

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