An implicit iterative algorithm with a tuning parameter for Itô Lyapunov matrix equations

References

• Bibby, J. (1974). Axiomatisations of the average and a further generalisation of monotonic sequences. Glasgow Mathematical Journal, 15, 63–65. doi:10.1017/S0017089500002135
   Web of Science ®Google Scholar
• Dehghan, M., & Hajarian, M. (2008). An iterative algorithm for the reflexive solutions of the generalized coupled Sylvester matrix equations and its optimal approximation. Applied Mathematics and Computation, 202, 571–588. doi:10.1016/j.amc.2008.02.035
   Web of Science ®Google Scholar
• Dehghan, M., & Hajarian, M. (2010a). The general coupled matrix equations over generalized bisymmetric matrices. Linear Algebra and its Applications, 432, 1531–1552. doi:10.1016/j.laa.2009.11.014
   Web of Science ®Google Scholar
• Dehghan, M., & Hajarian, M. (2010b). An iterative method for solving the generalized coupled Sylvester matrix equations over generalized bisymmetric matrices. Applied Mathematical Modelling, 34, 639–654. doi:10.1016/j.apm.2009.06.018
   Web of Science ®Google Scholar
• Deng, F. Q., Feng, Z. S., & Liu, Y. Q. (1996). Solution to matrix equation ATP + PA + ∑mi = 1FiTPFi = −Q with applications (In Chinese). Control Theory and Applications, 13, 163–168. Retrieved from http://navi.cnki.net
   Google Scholar
• Ding, F., & Chen, T. (2005). Gradient based iterative algorithms for solving a class of matrix equations. IEEE Transactions on Automatic Control, 50, 1216–1221. doi:10.1109/TAC.2005.852558
   Web of Science ®Google Scholar
• Ding, F., & Chen, T. (2006). On iterative solutions of general coupled matrix equations. SIAM Journal on Control and Optimization, 44, 2269–2284. doi:10.1137/S0363012904441350
   Web of Science ®Google Scholar
• Hajarian, M. (2013). Matrix iterative methods for solving the Sylvester-transpose and periodic Sylvester matrix equations. Journal of the Franklin Institute, 350, 3328–3341. doi:10.1016/j.jfranklin.2013.07.008
   Web of Science ®Google Scholar
• Hajarian, M. (2015). Matrix GPBiCG algorithms for solving the general coupled matrix equations. IET Control Theory & Applications, 9, 74–81. doi:10.1049/iet-cta.2014.0669
   Web of Science ®Google Scholar
• Hou, T., Zhang, W., & Ma, H. (2011). Essential instability and essential destabilisation of linear stochastic systems. IET Control Theory & Applications, 5, 334–340. doi:10.1049/iet-cta.2009.0655
   Web of Science ®Google Scholar
• Li, Z. Y., Wang, Y., Zhou, B., & Duan, G. R. (2010). On unified concepts of detectability and observability for continuous-time stochastic systems. Applied Mathematics and Computation, 217, 521–536. doi:10.1016/j.amc.2010.05.086
   Web of Science ®Google Scholar
• Li, Z. Y., Zhou, B., Lam, J., & Wang, Y. (2011). Positive operator based iterative algorithms for solving Lyapunov equations for Ito stochastic systems with Markovian jumps. Applied Mathematics and Computation, 217, 8179–8195. doi:10.1016/j.amc.2011.01.031
   Web of Science ®Google Scholar
• Rami, M. A., & Zhou, X. Y. (2000). Linear matrix inequalities, Riccati equations, and indefinite stochastic linear quadratic controls. IEEE Transactions on Automatic Control, 45, 1131–1143. doi:10.1109/9.863597
   Web of Science ®Google Scholar
• Wu, A. -G., Duan, G. -R., & Liu, W. (2016). Implicit iterative algorithms for continuous Markovian jump Lyapunov equations. IEEE Transactions on Automatic Control, 61, 3183–3189. doi:10.1109/TAC.2015.2508884
   Web of Science ®Google Scholar
• Xie, L., Ding, J., & Ding, F. (2009). Gradient based iterative solutions for general linear matrix equations. Computers & Mathematics with Applications, 58, 1441–1448. doi:10.1016/j.camwa.2009.06.047
   Web of Science ®Google Scholar
• Zhang, W., & Chen, B. S. (2004). On stabilizability and exact observability of stochastic systems with their applications. Automatica, 41, 87–94. doi:10.1016/j.automatica.2003.07.002
   Web of Science ®Google Scholar
• Zhang, W., Zhang, H., & Chen, B. S. (2008). Generalized Lyapunov equation approach to state-dependent stochastic stabilization/detectability criterion. IEEE Transactions on Automatic Control, 53, 1630–1642. doi:10.1109/TAC.2008.929368
   Web of Science ®Google Scholar
• Zhou, B., Duan, G. R., & Li, Z. Y. (2009). Gradient based iterative algorithm for solving coupled matrix equations. Systems & Control Letters, 58, 327–333. doi:10.1016/j.sysconle.2008.12.004
   Web of Science ®Google Scholar