References
- Amin S., Hante F., & Bayen A. (2012). Exponential stability of switched linear hyperbolic initial-boundary value problems. IEEE Transactions on Automatic Control, 57(2), 291–301. https://doi.org/https://doi.org/10.1109/TAC.2011.2158171
- Bao L., Fei S., & Yu L. (2014). Exponential stability of linear distributed parameter switched systems with time-delay. Journal of Systems Science and Complexity, 27(2), 263–275. https://doi.org/https://doi.org/10.1007/s11424-014-3070-4
- Bao, L., Wang, P., & Wang, X. (2019). Asymptotical stability of distributed parameter switched delay systems. Journal of Gui Zhou University, 36(4), 74–79. https://doi.org/https://doi.org/10.15958/j.cnki.gdxbzrb.2019.04.14
- Boyd S., Ghaoui L., Feron E., & Balakrishnan V. (1994). Linear matrix inequalities in system and control theory. SIAM.
- Branicky M. (1998). Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Transactions on Automatic Control, 43(4), 475–482. https://doi.org/https://doi.org/10.1109/9.664150
- Briat C. (2016). Convex lifted conditions for robust L2-stability analysis and L2-stabilization of linear discrete-time switched systems with minimum dwell-time constraint. Automatica, 50(3), 976–983. https://doi.org/https://doi.org/10.1016/j.automatica.2013.12.037
- Clason C., Rundb A., Kunisch K., & Barnard R. (2016). A convex penalty for switching control of partial differential equations. Systems & Control Letters, 89, 66–73. https://doi.org/https://doi.org/10.1016/j.sysconle.2015.12.013
- Cui, B., Deng, F., Wang, W., & Liu, Y. (2003). Exponential asymptotical stability for distributed parameter systems with time delays. Systems Engineering and Electronics, 25(5), 579–583. https://doi.org/https://doi.org/10.3321/j.issn:1001-506X.2003.05.019
- Cui B., & Lou X. (2009). Theory and applications of distributed parameter system with time-delay. National Defense Industry Press.
- Dong, X., Wen, R., & Liu, H. (2010). Robust fault-tolerant control for a class of distributed parameter switched system with time-delay. Journal of Control and Decision, 25(10), 1441–1450. https://doi.org/https://doi.org/10.3182/20130708-3-CN-2036.00003
- Dong, X., Wen, R., & Liu, H. (2011). Feedback stabilization for a class of distributed parameter switched systems with time delay. Journal of Applied Sciences, 29(1), 92–96. https://doi.org/https://doi.org/10.3969/j.issn.0255-8297.2011.01.016
- Espitia, N., Polyakov, A., & Fridman, E. (2019, December 11th-13th). On local finite-time stabilization of the Viscous Burgers equation via boundary switched linear feedback. CDC 2019-58th IEEE Conference on Decision and Control, Nice, France.
- Fridman E., & Orlov Y. (2009a). An LMI approach to H∞ boundary control of semilinear parabolic and hyperbolic systems. Automatica, 45(9), 2060–2066. https://doi.org/https://doi.org/10.1016/j.automatica.2009.04.026
- Fridman E., & Orlov Y. (2009b). Exponential stability of linear distributed parameter systems with time-varying delays. Automatica, 45(1), 194–201. https://doi.org/https://doi.org/10.1016/j.automatica.2008.06.006
- Gu K., Kharitonov V., & Chen J. (2003). Stability of time-delay systems. Birkhauser.
- Hante F., & Sigalotti M. (2011). Converse Lyapunov theorems for switched systems in Banach and Hilbert spaces. SIAM Journal on Control and Optimization, 49(2), 752–770. https://doi.org/https://doi.org/10.1137/100801561
- Jiang B., Shen Q., & Shi P. (2015). Neural-networked adaptive tracking control for switched nonlinear pure-feedback systems under arbitrary switching. Automatica, 61, 119–125. https://doi.org/https://doi.org/10.1016/j.automatica.2015.08.001
- Kundu A., & Chatterjee D. (2015). Stabilizing switching signals for switched systems. IEEE Transactions on Automatic Control, 60(3), 882–888. https://doi.org/https://doi.org/10.1109/TAC.2014.2335291
- Li Y., Chen C., & Wang B. (2019). Stabilization for Markovian jump distributed parameter systems with time delay. IEEE Access, 7, 103931–103937. https://doi.org/https://doi.org/10.1109/Access.6287639
- Li S., Kang W., & Ding D. (2019, June 3rd–5th). Observer-based H∞ fuzzy controlfor 1-D parabolic PDEs using point measurements. 2019 Chinese Control and Decision Conference (CCDC), Nanchang, China.
- Liberzon D. (2003). Switching in systems and control. Birkhauser.
- Liberzon D., & Morse A. (1999). Basic problems in stability and design of switched systems. IEEE Control Systems, 19(5), 59–70. https://doi.org/https://doi.org/10.1109/37.793443
- Lin H., & Antsaklis P. J. (2009). Stability and stabilizability of switched linear systems: A survey of recent results. IEEE Transactions on Automatic Control, 54(2), 308–322. https://doi.org/https://doi.org/10.1109/TAC.2008.2012009
- Luo, Y., Deng, F., & Liu, G. (2005). LMI-based approach for stabilization of distributed parameter control systems with delay. Control and Decision, 20(6), 625–633. https://doi.org/https://doi.org/10.13195/j.cd.2005.06.25.luoyp.006.
- Luo, Y., Xia, W., Liu, G., & Deng, F. (2009). LMI approach to exponential stabilization of distributed parameter control systems with delay. Acta Automatica Sinica, 35(3), 299–304. https://doi.org/https://doi.org/10.1016/S1874-1029(08)60078-6.
- Mei, M. (2009). Stability of traveling wavefronts for time-delayed reaction-diffusion equations. Discrete and Continuous Dynamical Systems, 526–535.
- Orlov Y., Lou Y., & Christodes P. (2004). Robust stabilization of infinite dimensional systems using sliding-mode output feedback control. International Journal of Control, 77(12), 1115–1136. https://doi.org/https://doi.org/10.1080/0020717042000273078
- Peitz S., & Klus S. (2019). Koopman operator-based model reduction for switched-system control of PDEs. Automatica, 106, 184–191. https://doi.org/https://doi.org/10.1016/j.automatica.2019.05.016
- Prieur C., Girard A., & Witrant E. (2014). Stability of switched linear hyperbolic systems by Lyapunov techniques. IEEE Transactions on Automatic Control, 59(8), 2196–2202. https://doi.org/https://doi.org/10.1109/TAC.2013.2297191
- Sasane, A. (2005). Stability of switching infinite-dimensional systems. Automatica, 41(1), 75–78. https://doi.org/https://doi.org/10.1016/j.automatica.2004.07.013
- Solomon O., & Fridman E. (2015). Stability and passivity analysis of semilinear diffusion PDEs with time-delays. International Journal of Control, 88(1), 180–192. https://doi.org/https://doi.org/10.1080/00207179.2014.942882
- Sun Z., & Ge S. (2005). Switched linear systems: Control and design. Springer-Verlag.
- Sun X., Zhao J., & Hill D. J. (2006). Stability and L2-gain analysis for switched delay systems: A delay-dependent method. Automatica, 42(10), 1769–1774. https://doi.org/https://doi.org/10.1016/j.automatica.2006.05.007
- Suyama K., & Sebe N. (2019). Switching L2 gain for evaluating the fluctuations in transient responses after an unpredictable system switch. International Journal of Control, 92(5), 1084–1093. https://doi.org/https://doi.org/10.1080/00207179.2017.1381884
- Tai Z., & Lun S. (2012). Absolutely exponential stability of Lure distributed parameter control systems. Applied Mathematics Letters, 25(3), 232–236. https://doi.org/https://doi.org/10.1016/j.aml.2011.07.010
- Wang J. (2019). A unified Lyapunov-based design for a dynamic compensator of linear parabolic MIMO PDEs. International Journal of Control. https://doi.org/https://doi.org/10.1080/00207179.2019.1676469
- Wang J., & Wu H. (2015). Some extended Wirtinger's inequalities and distributed proportional-spatial integral control of distributed parameter systems with multi-time delays. Journal of the Franklin Institute, 352(10), 4423–4445. https://doi.org/https://doi.org/10.1016/j.jfranklin.2015.06.011
- Wang J., Wu H., & Huang T. (2016). Passivity-based synchronization of a class of complex dynamical networks with time-varying delay. Automatica, 56, 105–112. https://doi.org/https://doi.org/10.1016/j.automatica.2015.03.027
- Wang H., & Xie L. (2019). Convergence analysis of a least squared algorithm of linear switched identification. Journal of Control and Decision, 1–18. https://doi.org/https://doi.org/10.1080/23307706.2019.1623097
- Wu H., Wang H., & Guo L. (2016). Disturbance rejection fuzzy control for nonlinear parabolic PDE systems via multiple observers. IEEE Transactions on Fuzzy Systems, 24(6), 1334–1348. https://doi.org/https://doi.org/10.1109/TFUZZ.2016.2514532
- Wu H., Wang J., & Li H. (2012). Exponential stabilization for a class of nonlinear parabolic PDE systems via fuzzy control approach. IEEE Transactions on Fuzzy Systems, 20(2), 318–329. https://doi.org/https://doi.org/10.1109/TFUZZ.2011.2173694
- Yang H., & Jiang B. (2013). On stability of nonlinear and switched parabolic systems.
- Zhai G., Hu B., Yasuda K., & Michel A. (2001a). Disturbance attenuation properties of time-controlled switched system. Journal of the Franklin Institute, 338(7), 765–779. https://doi.org/https://doi.org/10.1016/S0016-0032(01)00030-8
- Zhai G., Hu B., Yasuda K., & Michel A. (2001b). Stability analysis of switched systems with stable and unstable subsystems: An average dwell time approach. International Journal of Systems Science, 32(8), 1055–1061. https://doi.org/https://doi.org/10.1080/00207720116692
- Zhai G., Sun Y., Chen X., & Michel A. (2003). Stability and L2 gain analysis for switched symmetric systems with time delay. In Proceedings of American Control Conference, ACC meeting paper (pp. 4–6).
- Zhang W., & Yu L. (2009). Stability analysis for discrete-time switched time-delay systems. Automatica, 45(10), 2265–2271. https://doi.org/https://doi.org/10.1016/j.automatica.2009.05.027