ABSTRACT
Sylvester equations have found applications in many fields and have been investigated by numerous researchers. By searching the website www.amazon.com, we have found that there are over 300 books or book volumes, which use or involve Sylvester equations. Particularly, there are 38 books or book volumes which use GSEs, and these can be classified into the following categories:
■ Matrix algebra ◦ Matrix computation (Golub and Loan 1996, Higham 1996, Higham
2008) ◦ The matrix eigenvalue problem (van Dooren et al. 2001, Watkins 2007) ◦ Linear algebra and applications (Hazewinkel 1996, Moonen et al. 2010) ◦ Differential-algebraic equations (Ilchmann and Reis 2013) ◦ Algebraic geometry (Putinar and Sullivant 2010)
■ Numerical methods (Kressner 2005, Wachspress 2013) ■ Computer science
◦ Parallel computing (Ciegis et al. 2008, Fagerholm et al. 2002, Sorevik et al. 2001, 2006)
◦ Parallel processing (Danelutto et al. 2004, Kosch et al. 2003, Luque et al. 2008, Palma et al. 2001)
◦ High performance computing (Daydé et al. 2005). ■ Circuits and systems (Benner et al. 2005, Datta 1999, Srivastava et al. 2006) ■ Signal processing (Havelock et al. 2008, Leondes 1995) ■ Control systems
◦ Observer design (Trinh and Fernando 2011) ◦ Computer aided design (Anderson et al. 1999, Gray 2001) ◦ Descriptor linear systems (Duan 2010) ◦ Robust control design (Kucera and Sebek 2005) ◦ Periodic control systems (Bittanti and Colaneri 2002) ◦ Control designs (Skelton et al. 1997, Voicu 2003)
■ Biocomputing (Altman et al. 2006) ■ Life systems (Fei et al. 2010) ■ Neural networks (Liu et al. 2011)
In this chapter, we describe several typical applications of GSEs in linear control systems design, by only relating certain control design problems to GSEs.
