On the simultaneous stability of a finite set of matrices
by
R. Balaji
Department of Mathematics, Indian Institute of Technology Madras, Chennai-600036, India
Coauthors: V. Vetrivel (Department of Mathematics, Indian Institute of Technology Madras, Chennai-600036)

Given a linear operator L on the set S of all real symmetric square matrices of order n and Q in S, to the semidefinite linear complementarity problem SDLCP(L, Q) is to find a matrix X in S such that X and Y = L(X)+ Q are positive semidefinite and trace(XY ) = 0. In this article, we show that if A1, A2, · · ·An are simultaneously positive stable, then the SDLCP(L, Q) has a solution for all Q in S where L is the composition of the linear operators Ti (i = 1, 2, · · · n) where Ti(M) = AiM+MAi T- AiMAi T

Date received: November 12, 2004