Upper solution bound of the CCARE and its application in multi-agent systems with time-delay in the state

References

• Abdallah, C., Dorato, P., Benites-Read, J., & Byrne, R. (1993). Delayed positive feedback can stabilize oscillatory systems. In American Control Conference (pp. 3106–3107). IEEE.
   Google Scholar
• Aboudonia, A., Martinelli, A., & Lygeros, J. (2021). Passivity-based decentralized control for discrete-time large-scale systems. IEEE Control Systems Letters, 5(6), 2072–2077. https://doi.org/10.1109/LCSYS.7782633
   Google Scholar
• Basin, M., Rodriguez-Gonzalez, J., & Fridman, L. (2007). Optimal and robust control for linear state-delay systems. Journal of the Franklin Institute, 344(6), 830–845. https://doi.org/10.1016/j.jfranklin.2006.10.002
   Web of Science ®Google Scholar
• Berman, A., & Plemmons, R. J. (1994). Nonnegative matrices in the mathematical sciences. Society for Industrial and Applied Mathematics.
   Google Scholar
• Bernstein, D. S. (2005). Matrix mathematics: Theory, facts, and formulas with application to linear systems theory. Princeton University Press.
   Google Scholar
• Davies, R., Shi, P., & Wiltshire, R. (2008). Upper solution bounds of the continuous and discrete coupled algebraic Riccati equations. Automatica, 44(4), 1088–1096. https://doi.org/10.1016/j.automatica.2007.11.001
   Web of Science ®Google Scholar
• Fang, Y., & Loparo, K. (2002). Stabilization of continuous-time jump linear systems. IEEE Transactions on Automatic Control, 47(10), 1590–1603. https://doi.org/10.1109/TAC.2002.803528
   Web of Science ®Google Scholar
• Gantmakher, F. R. (2000). The theory of matrices. American Mathematical Society.
   Google Scholar
• Horn, R. A., & Johnson, C. R. (1990). Matrix analysis. Cambridge university press.
   Google Scholar
• Huo, X., Karimi, H. R., Zhao, X., Wang, B., & Zong, G. (2021). Adaptive-critic design for decentralized event-triggered control of constrained nonlinear interconnected systems within an identifier-critic framework. IEEE Transactions on Cybernetics, 99(2021), 1–14. https://doi.org/10.1109/TCYB.6221036
   Google Scholar
• Jiang, W., Chen, Y., & Charalambous, T. (2020). Consensus of general linear multi-agent systems with heterogeneous input and communication delays. IEEE Control Systems Letters, 5(3), 851–856. https://doi.org/10.1109/LCSYS.2020.3006452
   Google Scholar
• Lee, C. H. (1998). Simple stabilizability criteria and memoryless state feedback control design for time-delay systems with time-varying perturbations. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 45(11), 1211–1215. https://doi.org/10.1109/81.735446
   Google Scholar
• Lee, C. H. (2005). An improved lower matrix bound of the solution of the unified coupled Riccati equation. IEEE Transactions on Automatic Control, 50(8), 1221–1223. https://doi.org/10.1109/TAC.2005.852560
   Web of Science ®Google Scholar
• Li, Y., & Yu, K. (2021). Adaptive fuzzy decentralized sampled-data control for large-scale nonlinear systems. IEEE Transactions on Fuzzy Systems, 99, 1–14. https://doi.org/10.1109/TFUZZ.2021.3069321
   Web of Science ®Google Scholar
• Lin, C., & Nakamura, G. (2010). Unique continuation property for a coupled second-fourth order dynamical system and its application. SIAM Journal on Mathematical Analysis, 42(5), 2318–2336. https://doi.org/10.1137/090770357
   Web of Science ®Google Scholar
• Liu, J., & Wang, L. (2019). New solution bounds of the continuous algebraic Riccati equation and their applications in redundant control input systems. Sciece China: Information Sciences, 62(10). https://doi.org/10.1007/s11432-017-9553-5
   Web of Science ®Google Scholar
• Liu, J., Wang, L., & Zhang, J. (2016). The solution bounds and fixed point iterative algorithm for the discrete coupled algebraic Riccati equation applied to automatic control. IMA Journal of Mathematical Control and Information, 34(4), 1135–1156. https://doi.org/10.1093/imamci/dnw012
   Web of Science ®Google Scholar
• Liu, J., Wang, L., & Zhang, J. (2017a). New matrix bounds and iterative algorithms for the discrete coupled algebraic Riccati equation. International Journal of Control, 90(11), 2326–2337. https://doi.org/10.1080/00207179.2016.1245867
   Web of Science ®Google Scholar
• Liu, J., Wang, Y., & Zhang, J. (2017b). New upper matrix bounds with power form for the solution of the continuous coupled algebraic Riccati matrix equation. Asian Journal of Control, 19(2), 739–747. https://doi.org/10.1002/asjc.1400
   Web of Science ®Google Scholar
• Liu, J., & Zhang, J. (2012). New upper matrix bounds of the solution for perturbed continuous coupled algebraic Riccati matrix equation. International Journal of Control, Automation and Systems, 10(6), 1254–1259. https://doi.org/10.1007/s12555-012-0621-0
   Web of Science ®Google Scholar
• Liu, J., & Zhang, J. (2014). New upper and lower eigenvalue bounds for the solution of the continuous algebraic Riccati equation. Asian Journal of Control, 16(1), 284–291. https://doi.org/10.1002/asjc.2014.16.issue-1
   Web of Science ®Google Scholar
• Liu, T., Jiang, Z. P., & Zhang, P. (2020). Decentralized event-triggered control of large-scale nonlinear systems. International Journal of Robust and Nonlinear Control, 30(4), 1451–1466. https://doi.org/10.1002/rnc.v30.4
   Web of Science ®Google Scholar
• Muoz-Vázquez, A. J., & Sánchez-Torres, J. D. (2020). Predefined-time control of cooperative manipulators. International Journal of Robust and Nonlinear Control, 30(17), 7295–7306. https://doi.org/10.1002/rnc.v30.17
   Web of Science ®Google Scholar
• Nian, X., Su, S., & Pan, H. (2010). A BMI approach to the cooperative control of multi-agent systems and optimization. In Intelligent Control and Automation. IEEE.
   Google Scholar
• Orosz, G., Moehlis, J., & Murray, R. M. (2010). Controlling biological networks by time-delayed signals. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 368(1911), 439–454. https://doi.org/10.1098/rsta.2009.0242
   PubMed Web of Science ®Google Scholar
• Ostrowski, A., & Schneider, H. (1962). Some theorems on the inertia of general matrices. Journal of Mathematical analysis and applications, 4(1), 72–84. https://doi.org/10.1016/0022-247X(62)90030-6
   Google Scholar
• Su, X., Shi, P., Wu, L., & Song, Y. (2012). A novel approach to filter design for T–S fuzzy discrete-time systems with time-varying delay. IEEE Transactions on Fuzzy Systems, 20(6), 1114–1129. https://doi.org/10.1109/TFUZZ.2012.2196522
   Web of Science ®Google Scholar
• Wang, L. (2020). Refined upper solution bound of the continuous coupled algebraic Riccati equation. Complexity, 2020(2020), 1–12. https://doi.org/10.1155/2020/8627492
   Web of Science ®Google Scholar
• Xia, Y., Cai, C., Yin, M., & Zou, Y. (2015). Two new upper bounds of the solution for the continuous algebraic Riccati equation and their application. Science China: Information Science, 58(5), 150–161. https://doi.org/10.1007/s11432-014-5173-x
   Web of Science ®Google Scholar
• Yang, C., Liu, J., & Liu, Y. (2012). Solutions of the generalized Sylvester matrix equation and the application in eigenstructure assignment. Asian Journal of Control, 14(6), 1669–1675. https://doi.org/10.1002/asjc.v14.6
   Web of Science ®Google Scholar
• Yang, Z., & Fridman, E. (2020). Predictor methods for decentralized control of large-scale systems with input delays. Automatica, 116(4), 108903. https://doi.org/10.1016/j.automatica.2020.108903
   Web of Science ®Google Scholar
• Zhang, J., & Li, S. (2020). The structure-preserving doubling numerical algorithm of the continuous coupled algebraic Riccati equation. International Journal of Control, Automation and Systems, 18(7), 1641–1650. https://doi.org/10.1007/s12555-019-0368-y
   Web of Science ®Google Scholar
• Zhang, J., & Liu, J. (2013). The improved upper solution bounds of the continuous coupled algebraic Riccati matrix equation. International Journal of Control, Automation and Systems, 11(4), 852–858. https://doi.org/10.1007/s12555-012-0188-9
   Web of Science ®Google Scholar
• Zhang, K., Zhang, H., Cai, Y., & Su, R. (2019). Parallel optimal tracking control schemes for mode-dependent control of coupled Markov jump systems via integral RL method. IEEE Transactions on Automation Science and Engineering, 17(3), 1332–1342. https://doi.org/10.1109/TASE.2019.2948431
   Web of Science ®Google Scholar
• Zhao, Q., Ou, L., Shen, B., & Chen, J. (2014). Cooperative control of multi-agent system based on two-delay feedback. In Proceedings of the 33rd Chinese Control Conference (pp. 1710–1715).
   Google Scholar
• Zhou, K., Doyle, J. C., & Glover, K. (1996). Robust and optimal control. Prentice hall.
   Google Scholar
• Zhou, K., & Khargonekar, P. (1988). Robust stabilization of linear systems with norm-bounded time-varying uncertainty. Systems & Control Letters, 10(1), 17–20. https://doi.org/10.1016/0167-6911(88)90034-5
   Web of Science ®Google Scholar