219
Views
7
CrossRef citations to date
0
Altmetric
Original Articles

Passivity and H control of switched discrete-time nonlinear systems using linearisation

ORCID Icon & ORCID Icon
Pages 68-83 | Received 24 Nov 2016, Accepted 02 Oct 2017, Published online: 26 Oct 2017

References

  • Allerhand, L. I., & Shaked, U. (2013). Robust state-dependent switching of linear systems with dwell time. IEEE Transactions on Automatic Control, 58(4), 994–1001.
  • Atashzar, S. F., Shahbazi, M., Tavakoli, R. V., & Patel, R. (2017). A passivity-based approach for stable patient-robot interaction in haptics-enabled rehabilitation systems: Modulated time-domain passivity control. IEEE Transactions on Control Systems Technology, 25(3), 991–1006.
  • Byrnes, C. I., Isidori, A., & Willems, J. C. (1991). Passivity, feedback equivalence, and the global stabilization of minimum-phase nonlinear systems. IEEE Transactions on Automatic Control, 36(9), 1228–1240.
  • Dehghan, M., & Ong, C. J. (2012). Discrete-time switching linear system with constraints: Characterization and computation of invariant sets under dwell-time consideration. Automatica, 48, 964–969.
  • Duan, C., & Wu, F. (2014). Analysis and control of switched linear systems via dwell-time min-switching. Systems and Control Letters, 70(11), 8–16.
  • Hespanha, J. (2003). L2 induced gains of switched linear systems. In V. D. Blondel, A. Megretski (Eds.), Unsolved problems in mathematical systems and control theory (2nd ed., pp. 131–133). New Jersey, MA: Princeton University Press.
  • Hill, D. J., & Moylan, P. J. (1976). The stability of nonlinear dissipative systems. IEEE Transactions on Automatic Control, 21(5), 708–711.
  • Hill, D. J., & Moylan, P. J. (1980). Dissipative dynamical systems: Basic input-output and state properties. Journal of the Franklin Institute, 309(5), 327–357.
  • Lam, J., Shu, Z., & Mao, X. R. (2014). Stability analysis of continuous-time switched systems with a random switching signal. IEEE Transactions on Automatic Control, 59(1), 180–186.
  • Li, F. B., Wu, L. G., Shi, P., & Lim, C. C. (2015). State estimation and sliding mode control for semi-Markovian jump systems with mismatched uncertainties. Automatica, 51, 385–393.
  • Lian, J., Shi, P., & Feng, Z. (2013). Passivity and passification for a class of uncertain switched stochastic time-delay systems. IEEE Transactions on Cybernetics, 43(1), 3–13.
  • Lian, J., & Wang, J. (2015). Passivity of switched recurrent neural networks with time-varying delays. IEEE Transactions on Neural Networks and Learning Systems, 26(2), 357–366.
  • Lin, W., & Byrness, C. I. (1995). Passivity and absolute stabilization of a class of discrete time nonlinear systems. Automatica, 31(2), 263–267.
  • Liu, H., Shen, Y., & Zhao, X. D. (2013). Finite-time stability for switched linear system based on state-dependent switching strategy. Journal of the Franklin Institute, 350, 541–555.
  • Ma, Y., Kawakami, H., & Tse, C. K. (2004). Bifurcation analysis of switched dynamical systems with periodically moving borders. IEEE Transactions on Circuits and Systems, 51(6), 1184–1193.
  • Matthias, A. M., & Daniel, L. (2012). Input/output-to-state stability and state-norm estimators for switched nonlinear system. Automatica, 48(9), 2029–2039.
  • Matthias, A. M., Pascal, M., & Frank, A. (2012). Model predictive control of switched nonlinear systems under average dwell-time. Journal of Process Control, 22(9), 1702–1710.
  • Mitsubori, K., & Saito, T. (1997). Dependent switched capacitor chaos generator and its synchronization. IEEE Transactions on Circuits and Systems, 44(12), 1122–1128.
  • Mizumoto, I., Ohdaira, S., & Iwai, Z. (2010). Output feedback strict passivity of discrete time nonlinear systems and adaptive control system design with a PFC. Automatica, 46(9), 1503–1509.
  • Pang, H. B., & Zhao, J. (2015). Robust passivity, feedback passification and global robust stabilisation for switched non-linear systems with structural uncertainty. IET Control Theory and Applications, 9(11), 1723–1730.
  • Ruiz, A., & Schaft, A. V. D. (1992). On passivity systems: From linearity to nonlinearity. In Proceedings of the 2nd IFAC symposium on nonlinear control systems design, (pp. 24–26). Bordeaux, France: Elsevier.
  • Shi, P., Li, F. B., Wu, L. G., & Lim, C. C. (2017). Neural network-based passive filtering for delayed neutral-type semi-markovian jump systems. IEEE Transactions on Neural Networks and Learning Systems, 28(9), 2101–2114.
  • Shi, P., Su, X. J., & Li, F. B. (2016). Dissipativity-based filtering for fuzzy switched systems with stochastic perturbation. IEEE Transactions on Automatic Control, 61(6), 1694–1699.
  • Son, J. D. (2015). A discrete-time stochastic model of searching and switching strategy in a customized service providing company. International Journal of Innovative Computing Information & Control, 11(5), 1681–1690.
  • Sun, D., Naghdy, F., & Du, H. P. (2017). Neural network-based passivity control of teleoperation system under time-varying delays. IEEE Transactions on Cybernetics, 47(7), 1666–1680.
  • Sun, X. M., Liu, G. P., Rees, K., & Wang, W. (2008). Delay-dependent stability for discrete systems with large delay sequence based on switching techniques. Automatica, 44(11), 2902–2908.
  • Wang, Y., Gupta, V., & Antsaklis, P. J. (2014). On passivity of a class of discrete-time switched nonlinear systems. IEEE Transactions on Automatic Control, 59(3), 629–702.
  • Wang, D., Shi, P., Wang, W., & Karimi, H. R. (2014). Non-fragile H∞ control for switched stochastic delay systems with application to water quality process. International Journal of Robust and Nonlinear Control, 24(11), 1677–1693.
  • Wang, Y. E., Sun, X. M., & Mazenc, F. (2016). Stability of switched nonlinear systems with delay and disturbance. Automatica, 69, 78–86.
  • Wang, D., Wang, Z. D., Li, G. Y., & Wang, W. (2016). Distributed filtering for switched nonlinear positive systems with missing measurements over sensor networks. IEEE Sensors Journal, 16(12), 4940–4948.
  • Wang, J. L., Wu, H. N., & Huang, T. W. (2015). Passivity-based synchronization of a class of complex dynamical networks with time-varying delay. Automatica, 56, 105–112.
  • Wang, J. L., Wu, H. N., Huang, T. W., Ren, S. Y., & Wu, J. (2017). Passivity of directed and undirected complex dynamical networks with adaptive coupling weights. IEEE Transactions on Neural Networks and Learning Systems, 28(8), 1827–1839.
  • Willems, J. C. (1972). Dissipative dynamical systems, part I: General theory. Archive for Rational Mechanics and Analysis, 45(5), 321–351.
  • Wu, Z. J., Karimi, H. Z., & Shi, P. (2016). Dissipativity-based small-gain theorems for stochastic network systems. IEEE Transactions on Automatic Control, 61(8), 2065–2078.
  • Wu, Y. Q., Su, H. Y., Lu, R. Q., Wu, Z. G., & Shu, Z. (2015). Passivity-based non-fragile control for Markovian jump systems with aperiodic sampling. Systems and Control Letters, 84, 35–43.
  • Xia, M., Antsaklis, P. J., Gupta, V., & McCourt, M. J. (2015). Determining passivity using linearization for systems with feedthrough terms. IEEE Transactions on Automatic Control, 60(9), 2536–2541.
  • Xiang, W. M., Xiao, J., & Mahmoud, M. S. (2014). H∞ filtering for switched discrete-time systems under asynchronous switching: A dwell-time dependent Lyapunov functional method. International Journal of Adaptive Control and Signal Processing, 29(8), 971–990.
  • Xiang, W. M., Xiao, J., & Zhai, G. S. (2015). Dissipativity and dwell time specifications of switched discrete-time systems and its applications in H∞ and robust passive control. Information Sciences, 320, 206–222.
  • Ye, Z. Y., Ji, H., & Zhang, H. (2016). Passivity analysis of Markovian switching complex dynamic networks with multiple time-varying delays and stochastic perturbations. Chaos, Solitons and Fractals, 83(1), 147–157.
  • Zefran, M., Bullo, F., & Stein, M. (2001). A notion of passivity for hybrid systems. In Proceedings of the 40th IEEE conference on decision and control, Orlando, FL, USA: IEEE (Vol. 1, pp. 768–773).
  • Zhai, G. S., Hu, B., Yasuda, K., & Michel, A. N. (2001). Disturbance attenuation properties of time-controlled switched systems. Journal of Franklin Institute, 338(9), 765–779.
  • Zhang, L. X., Zhuang, S., & Shi, P. (2015). Non-weighter quasi-time-dependent H∞ filtering for switched linear systems with persistent dwell-time. Automatica, 54, 201–209.
  • Zhao, J., & Hill, D. J. (2006). A notion of passivity for switched systems with state-dependent switching. Journal of Control Theory and Applications, 4(1), 70–75.
  • Zhao, J., & Hill, D. J. (2008). Passivity and stability of switched systems: A multiple storage function method. Systems and Control Letters, 57(2), 158–164.
  • Zong, G. D., Ren, H. L., & Hou, L. L. (2016). Finite-time stability of interconnected impulsive switched systems. IET Control Theory and Applications, 10(6), 648–654.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.