Iterative algorithms for discrete periodic Riccati 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
• Bittanti, S., Colaneri, P., & De Nicolao, G. (1988). Difference periodic Riccati equation for the periodic prediction problem. IEEE Transactions on Automatic Control, 33, 706–712. doi:10.1109/9.1286
   Web of Science ®Google Scholar
• Bittanti, S., Colaneri, P., & De Nicolao, G. (1990). An algebraic Riccati equation for the discrete-time periodic prediction problem. Systems & Control Letters, 14, 71–78. doi:10.1016/0167-6911(90)90084-8
   Web of Science ®Google Scholar
• Bolzern, P., & Colaneri, P. (1987). Inertia theorems for the periodic Lyapunov difference equation and periodic Riccati difference equation. Linear Algebra & Its Applications, 85, 249–265. doi:10.1016/0024-3795(87)90221-7
   Web of Science ®Google Scholar
• Borno, I., & Gajic, Z. (1995). Parallel algorithm for solving coupled algebraic Lyapunov equations of discrete-time jump linear systems. Computers & Mathematics with Applications, 30, 1–4. doi:10.1016/0898-1221(95)00119-J
   Web of Science ®Google Scholar
• Chen, T., & Francis, B. A. (1995). Optimal sampled-data control systems. London: Springer. doi:10.1007/978-1-4471-3037-6
   Google Scholar
• Dehghan, M., & Hajarian, M. (2010). On the reflexive and anti-reflexive solutions of the generalised coupled Sylvester matrix equations. International Journal of Systems Science, 41, 607–625. doi:10.1080/00207720903072357
   Web of Science ®Google Scholar
• Dehghan, M., & Hajarian, M. (2012). The generalised Sylvester matrix equations over the generalised bisymmetric and skew-symmetric matrices. International Journal of Systems Science, 43, 1580–1590. doi:10.1080/00207721.2010.549584
   Web of Science ®Google Scholar
• De Souza, C. (1989). Existence conditions and properties for the maximal periodic solution of periodic Riccati difference equations. International Journal of Control, 50, 731–742. doi:10.1080/00207178908953393
   Web of Science ®Google Scholar
• Duan, G. R. (2016). Linear systems theory (In Chinese). Beijing: Science Press.
   Google Scholar
• Grasselli, O. M., Menini, L., & Valigi, P. (2015). Output regulation, tracking and nominal decoupling with stability for uncertain linear periodic systems. European Journal of Control, 5, 138–156. doi:10.1016/S0947-3580(99)70148-2
   Web of Science ®Google Scholar
• Hajarian, M. (2015). Finite algorithms for solving the coupled Sylvester-conjugate matrix equations over reflexive and Hermitian reflexive matrices. International Journal of Systems Science, 46, 488–502. doi:10.1080/00207721.2013.790999
   Web of Science ®Google Scholar
• Hajarian, M. (2018a). Finding solutions for periodic discrete-time generalized coupled Sylvester matrix equations via the generalized BCR method. Transactions of the Institute of Measurement and Control, 40, 647–656. doi:10.1177/0142331216670719
   Web of Science ®Google Scholar
• Hajarian, M. (2018b). Periodic conjugate direction algorithm for symmetric periodic solutions of general coupled periodic matrix equations. Computers and Mathematics with Applications, 75, 4151–4178. doi:10.1016/j.camwa.2018.03.020
   Web of Science ®Google Scholar
• Lv, L., & Zhang, Z. (2017). Finite iterative solutions to periodic Sylvester matrix equations. Journal of the Franklin Institute, 354, 2358–2370. doi:10.1016/j.jfranklin.2017.01.004
   Web of Science ®Google Scholar
• Lv, L., Zhang, Z., & Zhang, L. (2017). A parametric poles assignment algorithm for second-order linear periodic systems. Journal of the Franklin Institute, 354, 8057–8071. doi:10.1016/j.jfranklin.2017.09.029
   Web of Science ®Google Scholar
• Lv, L., Zhang, Z., & Zhang, L. (2018). A periodic observers synthesis approach for LDP systems based on iteration. IEEE Access, 6, 8539–8546. doi:10.1109/ACCESS.2018.2802643
   Web of Science ®Google Scholar
• Nicolao, G. D. (1992). Cyclomonotonicity and stabilizability properties of solutions of the difference periodic Riccati equation. IEEE Transactions on Automatic Control, 37, 1405–1410. doi:10.1109/9.159582
   Web of Science ®Google Scholar
• Qian, Y. Y., & Pang, W. J. (2015). An implicit sequential algorithm for solving coupled Lyapunov equations of continuous-time Markovian jump systems. Automatica, 60, 245–250. doi:10.1016/j.automatica.2015.07.011
   Web of Science ®Google Scholar
• Varga, A. (1997). Periodic Lyapunov equations: Some applications and new algorithms. International Journal of Control, 67, 69–88. doi:10.1080/002071797224360
   Web of Science ®Google Scholar
• Wu, A., & Duan, G. (2015). New iterative algorithms for solving coupled Markovian jump Lyapunov equations. IEEE Transactions on Automatic Control, 60, 289–294. doi:10.1109/TAC.2014.2326273
   Web of Science ®Google Scholar
• Yan, W., & Bitmead, R. R. (1989). Decentralized control of multi-channel systems with direct control feedthrough. International Journal of Control, 49, 2057–2075. doi:10.1080/00207178908961372
   Web of Science ®Google Scholar
• Yan, W., & Bitmead, R. R. (1991). Control of linear discrete-time periodic systems: A decentralized control approach. Proceedings of 1991 American control conference (pp. 910–915). Boston, MA. doi:10.23919/ACC.1991.4791510
   Google Scholar
• Zhou, B., Duan, G. R., & Lin, Z. (2011). A parametric periodic Lyapunov equation with application in semi-global stabilization of discrete-time periodic systems subject to actuator saturation. Automatica, 47, 316–325. doi:10.1016/j.automatica.2010.10.011
   Web of Science ®Google Scholar
• Zhou, B., Lin, Z., & Duan, G. R. (2011). Lyapunov differential equation approach to elliptical orbital rendezvous with constrained controls. Journal of Guidance, Control, and Dynamics, 34, 345–358. doi:10.2514/1.52372
   Web of Science ®Google Scholar