Some properties of generalized Lyapunov equations

@article{Zhang2011SomePO,
  title={Some properties of generalized Lyapunov equations},
  author={Weihai Zhang and Bor-Sen Chen},
  journal={2011 Chinese Control and Decision Conference (CCDC)},
  year={2011},
  pages={3137-3141}
}
By means of the spectral analysis method, this paper studies a class of generalized Lyapunov equations (GLEs) arising from stochastic stability. A necessary and sufficient condition is given for the existence and uniqueness of the symmetric/skew-symmetric solutions of such GLEs. A sufficient condition for the GLEs have no and have more than one symmetric/skew-symmetric solution is also presented, respectively.