Common Lyapunov solutions for two matrices whose difference has rank one
作者： Thomas J. Laffey , Helena Šmigoc
DOI: 10.1016/J.LAA.2009.02.026
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摘要: Abstract Real stable matrices A and B with rank of - equal to one have a common Lyapunov solution if only their product AB has no real negative eigenvalue. This was proved by Shorten Narendra [R.N. Shorten, K.S. Narendra, On quadratic functions for pairs LTI systems whose system are in companion form, IEEE Trans. Automat. Control 48 (4) (2003) 618–621], proof is based on the fundamental results Kalman Lure’s problem. In this paper we give an alternative result its generalization general regular inertia case, case when complex.
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