DocumentCode :
3743683
Title :
A Convexity Embedded Necessary and Sufficient Condition for the Hurwitz stability of a Real Matrix using its elemental sign structure and qualitative determinant concept
Author :
Rama K. Yedavalli
Author_Institution :
Department of Mechanical and Aerospace Engineering, The Ohio State University, Columbus, 43210-1276, USA
fYear :
2015
Firstpage :
3999
Lastpage :
4004
Abstract :
In this paper, we highlight the importance of the `elemental sign structure´ of a matrix in its Hurwitz stability/instability assessment. The issue of determining conditions for the Hurwitz stability of a matrix is an age old topic of interest to engineers working with continuous time linear state space systems. However, the reason for revisiting this old issue is that the currently available conditions of stability, namely the Routh-Hurwitz test and the associated Kronecker Lyapunov matrix characteristic equation test (Fuller´s condition) do not possess convexity property with respect to stability. In this paper, we present an alternative to these famous conditions by making use of the sign structure of the matrix. The proposed new condition of stability combines the concepts of both Quantitative Determinant (involving eigenvalues) and the Qualitative Determinant (involving only the sign information of the matrix elements) and serves as an alternative way of assessing the stability of a matrix. This new necessary and sufficient condition with convexity property is deemed extremely helpful in solving the related problems of stability including the testing of robust stability of interval parameter matrix families, which has attracted intense attention and scrutiny in the last few decades. The implications and importance of this new condition with convexity property are discussed.
Keywords :
"Stability criteria","Eigenvalues and eigenfunctions","Asymptotic stability","Control theory","Joining processes","Focusing"
Publisher :
ieee
Conference_Titel :
Decision and Control (CDC), 2015 IEEE 54th Annual Conference on
Type :
conf
DOI :
10.1109/CDC.2015.7402841
Filename :
7402841
Link To Document :
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