Stability of discrete-time delayed impulsive linear systems with application to multi-tracking

References

• Barabsi, A.L., Albert, R., Jeong, H., & Bianconi, G. (2000). Power-law distribution of the world wide web. Science, 287, 2115a.
   Web of Science ®Google Scholar
• Balarko, C., Rajat, M., & Bikash, C.P. (2004). Wide-area measurement-based stabilizing control of power systems considering signal transmission delay. IEEE Transactions on Power Systems, 19, 1971–1979.
   Web of Science ®Google Scholar
• Basin, M.V., & Pinsky, M.A. (1998). Stability impulse control of faulted nonlinear systems. IEEE Transactions on Automatic Control, 43(11), 1604–1608.
   Web of Science ®Google Scholar
• Cai, C.H., & Teel, A.R. (2009). Characterizations of input-to-state stability for hybrid systems. Systems and Control Letters, 58, 47–53.
   Web of Science ®Google Scholar
• Chen, T.P., Liu, X.W., & Lu, W.L. (2007). Pinning complex networks by a single controller. IEEE Transactions on Circuits and Systems I: Regular Papers, 54(6), 1317–1326.
   Web of Science ®Google Scholar
• Chen, W.-H., & Zheng, W.X. (2011). Exponential stability of nonlinear time-delay systems with delayed impulse effects. Automatica, 47, 1075–1183.
   Web of Science ®Google Scholar
• Dashkovskiy, S., Kosmykov, M., Mironchenko, A., & Naujok, L. (2012). Stability of interconnected impulsive systems with and without time delays, using Lyapunov methods. Nonlinear Analysis: Hybrid Systems, 6(3), 899–915.
   Web of Science ®Google Scholar
• Dashkovskiy, S., & Mironchenko, A. (2013). Input-to-state stability of nonlinear impulsive systems. SIAM Journal on Control and Optimization, 51, 1962–1987.
   Web of Science ®Google Scholar
• Gielen, R.H., Lazar, M., & Kolmanovsky, I.V. (2012). Lyapunov methods for time-invariant delay difference inclusions. SIAM Journal on Control and Optimization, 50, 110–132.
   Web of Science ®Google Scholar
• Glass, L. (2001). Synchronization and rhythmic processes in physiology. Nature, 410(6825), 277–284.
   PubMed Web of Science ®Google Scholar
• Guan, Z.H., Hill, D.J., & Shen, X. (2005). On hybrid impulsive and switching systems and application to nonlinear control. IEEE Transactions on Automatic Control, 50(7), 1058–1062.
   Web of Science ®Google Scholar
• Haddad, W.M., Chellaboina, V-S., & Nersesov, S.G. (2006). Impulsive and hybrid dynamical systems, stability, dissipativity, and control. Princeton, NJ: Princeton University Press.
   Google Scholar
• Heemels, W.P.M.H., Teel, A.R., van de Wouw, N., & Nešić, D. (2010). Networked control systems with communication constraints: Tradeoffs between transmission intervals, delayes and performance. IEEE Transactions on Automatic Control, 55, 1781–1796.
   Web of Science ®Google Scholar
• Hespanha, J.P., Liberzon, D., & Teel, A.R. (2008). Lyapunov conditions for input-to-state stability of impulsive systems. Automatica, 44, 2735–2744.
   Web of Science ®Google Scholar
• Hespanha, J.P., & Morse, A.S. (1999). Stability of switched systems with average dwell-time. In Proceedings of the 38th IEEE Conference on Decision and Control (pp. 2655–2660). New York: IEEE.
   Google Scholar
• Hetel, L., Daafouz, J., & Iung, C. (2008). Equivalence between the Lyapunov-Krasovskii functionals approach for discrete delay systems and that of the stability conditions for switched systems. Nonlinear Analysis: Hybrid Systems, 2, 697–705.
   Web of Science ®Google Scholar
• Jiang, G.P., Tang, W.K.S., & Chen, G. (2006). A state-observer-based approach for synchronization in complex dynamical networks. IEEE Transactions on Circuits and Systems-I, 53(12), 2739–2745.
   Google Scholar
• Kolmanovskii, V., & Myshkis, A. (1999). Introduction to the theory and applications of functional differential equations. Dordrecht, The Netherlands: Kluwer Academic Publishers.
   Google Scholar
• Lakshmikantham, V., Bainov, D.D., & Simeonov, P.S. (1989). Theory of impulse differential equations. Singapore: World Scientific.
   Google Scholar
• Li, C., & Chen, G. (2004). Synchronization in general compelx dynamical networks with coupling delays. Physica A, 343, 263–278.
   Web of Science ®Google Scholar
• Li, Z.G., Wen, C.Y., & Soh, Y.C. (2001). Analysis and design of impulsive control systems. IEEE Transactions on Automatic Control, 46(6), 894–897.
   Web of Science ®Google Scholar
• Liu, B. (2008). Stability of solutions for stochastic impulsive systems via comparison approach. IEEE Transactions on Automatic Control, 53(9), 2128–2133.
   Web of Science ®Google Scholar
• Liu, B., & Hill, D.J. (2009). Comparison principle and stability of discrete impulsive hybrid systems. IEEE Transactions on Circuits and Systems-I (Regular Papers), 56(1), 233–245.
   Web of Science ®Google Scholar
• Liu, B., & Hill, D.J. (2011). Impulsive consensus for complex dynamical networks with nonidentical nodes and coupling time-delays. SIAM Journal on Control and Optimization, 49(2), 315–338.
   Web of Science ®Google Scholar
• Liu, B., Liu, X.Z., Chen, G., & Wang, H. (2005). Robust impulsive synchronization of uncertain dynamical networks. IEEE Transactions on Circuits and Systems-I, 52, 1431–1441.
   Google Scholar
• Liu, J., Liu, X.Z., & Xie, W.-C. (2011). Input-to-state stability of impulsive and switching hybrid systems with time-delay. Automatica, 47, 899–908.
   Web of Science ®Google Scholar
• Liu, B., & Marquez, H.J. (2007a). Quasi-exponential input-to-state stability for discrete-time impulsive hybrid systems. International Journal of Control, 80(4), 540–554.
   Web of Science ®Google Scholar
• Liu, B., & Marquez, H.J. (2007b). Razumikhin-type stability theorems for discrete delay systems. Automatica, 43, 1219–1225.
   Web of Science ®Google Scholar
• Liu, T., Zhao, J., & Hill, D.J. (2010). Exponential synchronization of complex delayed dynamical networks with switching topology. IEEE Transactions on Circuits and Systems-I, 57, 2967–2980.
   Google Scholar
• Lü, J., & Chen, G. (2005). A time-varying complex dynamical model and its controlled synchronization criteria. IEEE Transactions on Automatic Control, 50(6), 841–846.
   Web of Science ®Google Scholar
• Naghshtabrizi, P., Hespanha, J.P., & Teel, A.R. (2010). Stability of delay impulsive systems with application to networked control systems. Transactions of the Institute of Measurement and Control, Speical Issue on Hybrid and Switched Systems, 32, 511–528.
   Google Scholar
• Nešić, D., & Teel, A. (2004). Input-output stability properties of networked control systems. IEEE Transactions on Automatic Control, 49, 1650–1667
   Web of Science ®Google Scholar
• Newman, M.E.J. (2003). The structure and function of complex networks. SIAM Review, 45, 167–256.
   Web of Science ®Google Scholar
• Olfati-Saber, R., & Murray, R.M. (2004). Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control, 49, 1520–1533.
   Web of Science ®Google Scholar
• Pecora, L.M., & Carroll, T.L. (1990). Synchronization in chaotic systems. Physical Review Letters, 64(8), 821–824.
   PubMed Web of Science ®Google Scholar
• Polushin, I.G., & Marquez, H.J. (2008). On the model-based approach to nonlinear networked control systems. Automatica, 44, 2409–2414.
   Web of Science ®Google Scholar
• Rodrigues, H.M., Alberto, L.F.C., & Bretas, N.G. (2000). On the invariance principle: Generalizations and applications to synchronization. IEEE Transactions on Circuits and Systems-I, 47(5), 730–738.
   Google Scholar
• Strogatz, S.H., & Stewart, I. (1993). Coupled oscillators and biological synchronization. Scientific American, 269(6), 102–109.
   PubMed Web of Science ®Google Scholar
• Strogatz, S.H. (2001). Exploring complex networks. Nature, 410, 268–276.
   PubMed Web of Science ®Google Scholar
• Sun, J., Zhang, Y., & Wu, Q. (2003). Less conservation conditions of stability for impulsive control systems. IEEE Transactions on Automatic Control, 48, 829–831.
   Web of Science ®Google Scholar
• Tipsuwan, Y., & Chow, M.Y. (2003). Control methodologies in networked control systems. Control Engineering Practice, 11, 1099–1111.
   Web of Science ®Google Scholar
• van de Wouw, N., Nešić, D., & Heemels, W.P.M.H. (2010). Stability analysis of nonlinear networked control systems: A discrete-time approach. In Proceedings of the 49th IEEE Conference on Decision and Control (pp. 7557–7563). Atlanta, GA, Institute of Electrical and Electronics Engineers (IEEE).
   Google Scholar
• Xia, W., & Cao, M. (2011). Clustering in diffusively coupled networks. Automatica, 47, 2395–2405.
   Web of Science ®Google Scholar
• Ye, H., Michel, A.N., & Hou, L. (1998). Stability analysis of systems with impulse effects. IEEE Transactions on Automatic Control, 43, 1719–1723.
   Web of Science ®Google Scholar
• Zhang, W., Branicky, M.S., & Phillips, S.M. (2001). Stability of networked control systems. IEEE Control Systems Magazine, 21, 84–99.
   Web of Science ®Google Scholar
• Zhang, L., Shi, Y., Chen, T., & Huang, B. (2005). A new method for stabilization of networked control systems with random time delays. IEEE Transactions on Automatic Control, 50, 1177–1181.
   Web of Science ®Google Scholar
• Zhao, Y.-B., Liu, G.-P., & Rees, D. (2010). Stability and stabilization of discrete-time networked control systems: A new time delay systems approach. IET Control Theory and Applications, 4, 1859–1866.
   Web of Science ®Google Scholar