Title :
Controller Design and the Gauss–Lucas Theorem
Author :
Knap, M.J. ; Keel, L.H. ; Bhattacharyya, S.P.
Author_Institution :
Dept. of Math., Tennessee State Univ., Nashville, TN, USA
Abstract :
In this technical note, we demonstrate how the classical Gauss-Lucas theorem can aid in the determination of stabilizing controllers for feedback systems. Moreover, we show how to apply the Gauss-Lucas theorem in the construction of new necessary conditions for Schur and Hurwitz stability. The results are used to derive new bounds on the stability margins and performance of control systems.
Keywords :
control system synthesis; feedback; performance index; stability; Hurwitz stability; Schur stability; classical Gauss-Lucas theorem; control system performance; controller design; feedback systems; necessary conditions; stability margins; stabilizing controllers; Approximation methods; Closed loop systems; Educational institutions; Polynomials; Stability criteria; Gauss–Lucas theorem; Hurwitz stability; Schur stability;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2013.2258795
