Title :
Routh, Hurwitz, Bieler and Kharitonov: A unified approach using the Schwarz form
Author :
Shorten, Robert ; Narendra, K.S.
Author_Institution :
IBM Res. Ireland, Dublin, Ireland
Abstract :
The equivalence of the well known Routh and Hurwitz criteria and the conditions derived using a quadratic Lyapunov function, were established by Patrick Parks. In this paper it is shown that the basic mathematical framework used by him involving the Schwarz form can be used to derive the same stability conditions in a simple form, and that results due to Bieler and Kharitonov can also be derived in a unified fashion.
Keywords :
Lyapunov methods; linear systems; matrix algebra; polynomials; quadratic programming; stability; stability criteria; Bieler criteria; Hurwitz criteria; Kharitonov criteria; Routh criteria; Schwarz form; Schwarz matrix; linear time-invariant system; mathematical framework; quadratic Lyapunov function; stability conditions; Asymptotic stability; Eigenvalues and eigenfunctions; Lyapunov methods; Polynomials; Stability criteria; Transfer functions;
Conference_Titel :
American Control Conference (ACC), 2013
Conference_Location :
Washington, DC
Print_ISBN :
978-1-4799-0177-7
DOI :
10.1109/ACC.2013.6580107
