Infinite-dimensional Sylvester equations: Basic theory and application to observer design

Alber, J. (2001). On implemented semigroups, Semigroup Forum 63(3): 371-386.10.1007/s002330010082Search in Google Scholar

Arendt, W., Raebiger, F. and Sourour, A. (1994). Spectral properties of the operator equation ax + xb = y, Quarterly Journal of Mathematics 45(2): 133-149.10.1093/qmath/45.2.133Search in Google Scholar

Chen, C.-T. (1984). Linear Systems Theory and Design, Holt, Rinehart and Winston, New York, NY.Search in Google Scholar

Emirsajłow, Z. (2005). Implemented Semigroup in Analysis of Infinite-Dimensional Sylvester and Lyapunov equations, Technical University of Szczecin Press, Szczecin, (in Polish).Search in Google Scholar

Emirsajłow, Z. and Townley, S. (2000). From PDEs with a boundary control to the abstract state equation with an unbounded input operator, European Journal of Control 7(1): 1-23.10.1016/S0947-3580(00)70908-3Search in Google Scholar

Emirsajłow, Z. and Townley, S. (2005). On application of the implemented semigroup to a problem arising in optimal control, International Journal of Control 78(4): 298-310.10.1080/00207170500093960Search in Google Scholar

Engel, J. and Nagel, R. (2000). One-Parameter Semigroups for Linear Evolution Equations, Springer-Verlag, New York, NY.Search in Google Scholar

Gajic, Z. and Qureshi, M. (2000). Lyapunov Matrix Equation in Systems Stability and Control, Academic Press, San Diego, CA.Search in Google Scholar

Kuehnemund, F. (2001). Bi-continuous Semigroups on Spaces with Two Topologies: Theory and Applications, Ph.D. thesis, Eberhard-Karls-Univerität Tuebingen, Tuebingen.Search in Google Scholar

Phong, V. Q. (1991). The operator equation ax - xb = c with unbounded operators a and b and related Cauchy problems, Mathematische Zeitschrift 208(7): 567-588.10.1007/BF02571546Search in Google Scholar