An inertia theorem for Lyapunov's equation and the dimension of a controllability space

✍ Scribed by R. Loewy

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 342 KB
• Volume: 260
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(97)80002-x

✦ Synopsis

A be an n X n complex matrix with inertia In(A) = (r(A), a(A), s(A)), and let H be an n x n hermitian matrix with inertia In(H) = (r(H), 6(H), 6(H)). Let K b e an n X n positive semidefinite matrix such that K = AH + HA*. Suppose that 1 is the dimension of the controllability space of the pair (A, K). Lcrer and Rodman conjectured that llr( A) -P( H )I < n -1 and lt9( A) -I?( H )I < n -1. It is our purpose to prove this conjecture.