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Articles

Stability and convergence properties of forced infinite-dimensional discrete-time Lur'e systems

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Pages 3026-3049 | Received 17 Oct 2018, Accepted 23 Jan 2019, Published online: 22 Feb 2019

References

  • Angeli, D. (2002). A Lyapunov approach to incremental stability properties. IEEE Transactions on Automatic Control, 47(3), 410–421.
  • Arcak, M., & Teel, A. (2002). Input-to-state stability for a class of Lurie systems. Automatica, 38(11), 1945–1949.
  • Bill, A., Guiver, C., Logemann, H., & Townley, S. (2016). Stability of nonnegative Lur'e systems. SIAM Journal on Control and Optimization, 54(3), 1176–1211.
  • Bill, A., Guiver, C., Logemann, H., & Townley, S. (2017). The converging-input converging-state property for Lur'e systems. Mathematics of Control, Signals, and Systems, 29, 4. Retrieved from https://doi.org/10.1007/s00498-016-0184-3.
  • Briggs, J., Dabbs, K., Holm, M., Lubben, J., Rebarber, R., Tenhumberg, B., & Riser-Espinoza, D. (2010). Structured population dynamics: An introduction to integral modeling. Mathematics Magazine, 83(4), 243–257.
  • Childs, D. Z., Rees, M., Rose, K. E., Grubb, P. J., & Ellner, S. P. (2003). Evolution of complex flowering strategies: An age- and size-structured integral projection model. Proceedings of the Royal Society of London. Series B: Biological Sciences, 270(1526), 1829–1838.
  • Curtain, R. F., & Zwart, H. (1995). An introduction to infinite-dimensional linear systems theory. New York: Springer-Verlag.
  • Dashkovskiy, S. N., Efimov, D. V., & Sontag, E. D. (2011). Input-to-state stability and related properties of systems. Avtomatika i Telemekhanika, 72(8), 3–40.
  • Dashkovskiy, S. N., & Mironchenko, A. (2013). Input-to-state stability of infinite-dimensional control systems. Mathematics of Control, Signals, and Systems, 25(1), 1–35.
  • Dashkovskiy, S. N., Rüffer, B. S., & Wirth, F. R. (2007). An ISS small gain theorem for general networks. Mathematics of Control, Signals, and Systems, 19(2), 93–122.
  • Eager, E. A., Rebarber, R., & Tenhumberg, B. (2012). Choice of density-dependent seedling recruitment function affects predicted transient dynamics: A case study with Platte thistle. Theoretical Ecology, 5(3), 387–401.
  • Easterling, M. R., Ellner, S. P., & Dixon, P. M. (2000). Size-specific sensitivity: Applying a new structured population model. Ecology, 81(3), 694–708.
  • Ellner, S. P., & Rees, M. (2006). Integral projection models for species with complex demography. The American Naturalist, 167(3), 410–428.
  • Franco, D., Guiver, C., Logemann, H., & Peràn, J. (2018). A class of forced nonlinear infinite-dimensional population models: Boundedness, persistence and stability. Submitted.
  • Guiver, C., Logemann, H., & Opmeer, M. R. (2017). Transfer functions of infinite-dimensional systems: positive realness and stabilization. Mathematics of Control, Signals, and Systems, 29, 20. Retrieved from https://doi.org/10.1007/s00498-017-0203-z.
  • Guiver, C., Logemann, H., & Opmeer, M. R. (2019). Infinite-dimensional Lur'e systems: Input-to-state stability and convergence properties. SIAM Journal on Control and Optimization, 57(1), 334–365.
  • Hinrichsen, D., & Pritchard, A. J. (2005). Mathematical systems theory I. Berlin: Springer-Verlag.
  • Jacob, B., Nabiullin, R., Partington, J. R., & Schwenninger, F. L. (2018). Infinite-dimensional input-to-state stability and Orlicz spaces. SIAM Journal on Control and Optimization, 56(2), 868–889.
  • Jayawardhana, B., Logemann, H., & Ryan, E. P. (2009). Input-to-state stability of differential inclusions with applications to hysteretic and quantized feedback systems. SIAM Journal on Control and Optimization, 48(2), 1031–1054.
  • Jayawardhana, B., Logemann, H., & Ryan, E. P. (2011). The circle criterion and input-to-state stability: New perspectives on a classical result. IEEE Control Systems Magazine, 31(4), 32–67.
  • Jiang, Z.-P., Teel, A. R., & Praly, L. (1994). Small-gain theorem for ISS systems and applications. Mathematics of Control, Signals, and Systems, 7(2), 95–120.
  • Jiang, Z.-P., & Wang, Y. (2001). Input-to-state stability for discrete-time nonlinear systems. Automatica, 37(6), 857–869.
  • Jiang, Z.-P., & Wang, Y. (2002). A converse Lyapunov theorem for discrete-time systems with disturbances. Systems & Control Letters, 45(1), 49–58.
  • Jiang, Z.-P., & Wang, Y. (2005). Nonlinear small-gain theorems for discrete-time feedback systems and applications. Automatica, 40(12), 2125–2136.
  • Khalil, H. K. (2002). Nonlinear systems (3rd ed.). Upper Saddle River: Prentice-Hall.
  • Lax, P. D. (2002). Functional analysis. New York: John Wiley and Sons.
  • Liberzon, M. R. (2006). Essays on the absolute stability theory. Automation and Remote Control, 67(10), 1610–1644.
  • Logemann, H. (2013). Stabilization of well-posed infinite-dimensional systems by dynamic sampled-data feedback. SIAM Journal on Control and Optimization, 51(2), 1203–1231.
  • Logemann, H., Rebarber, R., & Townley, S. (2003). Stability of infinite-dimensional sampled-data systems. Transactions of the American Mathematical Society, 355(8), 3301–3329.
  • Logemann, H., Rebarber, R., & Townley, S. (2005). Generalized sampled-data stabilization of well-posed linear infinite-dimensional systems. SIAM Journal on Control and Optimization, 44(4), 1345–1369.
  • Logemann, H., Ryan, E. P., & Townley, S. (1999). Integral control of linear systems with actuator nonlinearities: Lower bounds for the maximal regulating gain. IEEE Transactions on Automatic Control, 44(6), 1315–1319.
  • MATLAB Release (2014). The MathWorks, Inc., Natick, Massachusetts, United States.
  • Merow, C., Dahlgren, J. P., Metcalf, C. J. E., Childs, D. Z., Evans, M. E., Jongejans, E., … McMahon, S. M. (2014). Advancing population ecology with integral projection models: A practical guide. Methods in Ecology and Evolution / British Ecological Society, 5(2), 99–110.
  • Mironchenko, A., Karafyllis, I., & Krstic, M. (2017). Monotonicity methods for input-to-state stability of nonlinear parabolic PDEs with boundary disturbancess. arXiv:1706.07224.
  • Mironchenko, A., & Wirth, F. (2018). Characterizations of input-to-state stability for infinite-dimensional systems. IEEE Transactions on Automatic Control, 63(6), 1692–1707.
  • Pazy, A. (1983). Semigroups of linear operators and applications to partial differential equations. New York: Springer-Verlag.
  • Pepe, P., & Jiang, Z. P. (2006). A Lyapunov-Krasovskii methodology for ISS and iISS of time-delay systems. Systems & Control Letters, 55(12), 1006–1014.
  • Prieur, C., & Mazenc, F. (2012). ISS-Lyapunov functions for time-varying hyperbolic systems of balance laws. Mathematics of Control, Signals, and Systems, 24(1–2), 111–134.
  • Rose, K. E., Louda, S. M., & Rees, M. (2005). Demographic and evolutionary impacts of native and invasive insect herbivores on Cirsium canescens. Ecology, 86(2), 453–465.
  • Rosen, I. G., & Wang, C. (1992). On stabilizability and sampling for infinite-dimensional systems. IEEE Transactions on Automatic Control, 37(10), 1653–1656.
  • Rudin, W. (1987). Real and complex analysis (3rd ed.). New York: McGraw-Hill.
  • Sarkans, E., & Logemann, H. (2015). Input-to-state stability of Lur'e systems. Mathematics of Control, Signals, and Systems, 27(4), 439–465.
  • Sarkans, E., & Logemann, H. (2016a). Stability of higher-order discrete-time Lur'e systems. Linear Algebra and its Applications, 506, 183–211.
  • Sarkans, E., & Logemann, H. (2016b). Input-to-state stability of discrete-time Lur'e systems. SIAM Journal on Control and Optimization, 54(3), 1739–1768.
  • Sontag, E. D. (1989). Smooth stabilization implies coprime factorization. IEEE Transactions on Automatic Control, 34(4), 435–443.
  • Sontag, E. D. (1998). Comments on integral variants of ISS. Systems & Control Letters, 34(1–2), 93–100.
  • Sontag, E. D. (2008). Input to state stability: Basic concepts and results. In P. Nistri and G. Stefani (Eds.), Lecture notes in mathematics: Vol. 1932. Nonlinear and optimal control theory (pp. 163–220). Berlin: Springer.
  • Sontag, E. D., & Wang, Y. (1995). On characterizations of the input-to-state stability property. Systems & Control Letters, 24(5), 351–359.
  • Sontag, E. D., & Wang, Y. (1997). New characterizations of input-to-state stability. IEEE Transactions on Automatic Control, 41(9), 1283–1294.
  • Vidyasagar, M. (2002). Nonlinear systems analysis. Philadelphia, PA: SIAM.

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