On integral input-to-state stability for a feedback interconnection of parameterised discrete-time systems

References

• Angeli, D. (1999). Intrinsic robustness of global asymptotic stability. Systems & Control Letter, 38, 297–307.
   Web of Science ®Google Scholar
• Angeli, D., Sontag, E.D., & Wang, Y. (2000). A characterization of integral input-to-state stability. IEEE Transactions on Automatic Control, 45, 1082–1097.
   Web of Science ®Google Scholar
• Coron, J.-M., Praly, L., & Teel, A. (1994). Feedback stabilization of nonlinear systems: Sufficient conditions and Lyapunov and input-output techniques. In A. Isidori (Ed.), Trends in control (pp. 293–348). London: Springer.
   Google Scholar
• Dashkovskiy, S., Karimi, H.R., & Kosmykov, M. (2012). A Lyapunov-Razumikhin approach for stability analysis of logistics networks with time-delays. International Journal of Systems Science, 43, 845–853.
   Web of Science ®Google Scholar
• Dashkovskiy, S., Karimi, H.R., & Kosmykov, M. (2013). Stability analysis of logistics networks with time-delays. Journal of Production Planning $\&$ Control, 24, 567–574.
   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
• Dashkovskiy, S., Rüffer, B.S., & Wirth, F.R. (2005). A small-gain type stability criterion for large scale networks of ISS systems. In Proceedings of the 48th IEEE Conference on Decision Control (pp. 5633–5638). Seville, Spain.
   Google Scholar
• Dashkovskiy, S., Rüffer, B.S., & Wirth, F.R. (2007). An ISS small gain theorem for general networks. Mathematics of Control, Signals, and Systems, 19, 93–122.
   Web of Science ®Google Scholar
• Dashkovskiy, S., Rüffer, B.S., & Wirth, F.R. (2010). Small gain theorems for large scale systems and construction of ISS Lyapunov functions. SIAM Journal on Control and Optimization, 48, 4089–4118.
   Web of Science ®Google Scholar
• Ito, H. (2006). State-dependent scaling problems and stability of interconnected iISS and ISS systems. IEEE Transactions on Automatic Control, 51, 1626–1643.
   Web of Science ®Google Scholar
• Ito, H., Dashkovskiy, S., & Wirth, F. (2009). On a small gain theorem for networks of iISS systems. In Proceedings of the 48th IEEE Conference on Decision Control (pp. 4210–4215). Shanghai.
   Google Scholar
• Ito, H., & Jiang, Z.-P. (2009). Necessary and sufficient small gain conditions for integral input-to-state stable systems: A Lyapunov perspective. IEEE Transactions on Automatic Control, 54, 2389–2404.
   Web of Science ®Google Scholar
• Ito, H., Jiang, Z.-P., Dashkovskiy, S., & Rüffer, B.S. (2013). Robust stability of networks of iISS systems: Construction of sum-type Lyapunov functions. IEEE Transactions on Automatic Control, 58, 1192–1207.
   Web of Science ®Google Scholar
• Ito, H., Pepe, P., & Jiang, Z.-P. (2010). A small-gain condition for iISS of interconnected retarded systems based on Lyapunov-Krasovskii functionals. Automatica, 46, 1646–1656.
   Web of Science ®Google Scholar
• Jiang, Z.-P., Marlees, I., & Wang, Y. (1996). A Lyapunov formulation of the nonlinear small-gain theorem for interconnected ISS systems. Automatica, 32, 1211–1215.
   Web of Science ®Google Scholar
• Jiang, Z.-P., Teel, A.R., & Praly, L. (1994). Small-gain theorem for ISS systems and applications. Mathematics of Control, Signals, and Systems, 7, 95–120.
   Web of Science ®Google Scholar
• Jiang, Z.-P., & Wang, Y. (2001). Input-to-state stability for discrete-time nonlinear systems. Automatica, 37, 857–869.
   Web of Science ®Google Scholar
• Jiang, Z.-P., & Wang, Y. (2003). Small gain theorems on input-to-output stability. In Proceedings of the 3rd International DCDIS Conference (pp. 220–224). Guelph, Canada.
   Google Scholar
• Khalil, H. (2002). Nonlinear systems (3rd ed.). Eaglewood Cliffs, NJ: Prentice-Hall.
   Google Scholar
• Laila, D.S., & Nešić, D. (2004). Discrete-time Lyapunov based small-gain theorem for parameterized interconnected ISS systems. IEEE Transactions on Automatic Control, 48, 1783–1788.
   Web of Science ®Google Scholar
• Liberzon, D., Nešić, D., & Teel, A.R. (2014). Lyapunov-based small-gain theorems for hybrid systems. IEEE Transactions on Automatic Control, 59, 1395–1410.
   Google Scholar
• Loria, A., & Nešić, D. (2003). On uniform boundedness of parameterized discrete-time systems with decaying inputs: Applications to cascades. Systems & Control Letters, 49, 163–174.
   Web of Science ®Google Scholar
• Loria, A., & Nešić, D. (2004). On uniform asymptotic stability of time-varying parameterized discrete-time cascades. IEEE Transactions on Automatic Control, 49, 875–887.
   Web of Science ®Google Scholar
• Nešić, D., & Teel, A.R. (2001). Changing supply functions in input to state stable systems: The discrete-time case. IEEE Transactions on Automatic Control, 45, 960–962.
   Google Scholar
• Sanfelice, R.G. (2010). Results on input-to-output and input-output-to-state stability for hybrid systems and their interconnections. In Proceedings of the 49th IEEE Conference on Decision Control (pp. 2396–2401). Atlanta, GA.
   Google Scholar
• Sontag, E.D. (1998). Comments on integral variants of ISS. Systems & Control Letter, 34, 93–100.
   Web of Science ®Google Scholar
• Sontag, E.D., & Teel, A.R. (1995). Changing supply functions in input/state stable systems. IEEE Transactions on Automatic Control, 40, 1476–1478.
   Web of Science ®Google Scholar