Skip to main content

Measurable Disturbance Decoupling for Impulsive Switching Linear Systems

  • Conference paper
  • First Online:
15th European Workshop on Advanced Control and Diagnosis (ACD 2019) (ACD 2019 2018)

Part of the book series: Lecture Notes in Control and Information Sciences - Proceedings ((LNCOINSPRO))

Included in the following conference series:

  • 501 Accesses

Abstract

This work deals with the problem of annihilating the effect of a disturbance accessible for measurement on the output of an impulsive switching linear system—i.e., a hybrid system whose state is affected by discontinuities at the same instants when its dynamics is subject to switches. Jumping and switching are assumed to be immediately detectable and to satisfy a minimum dwell time requisite. The information available on the disturbance is exploited by resorting to a feedforward compensation scheme. A necessary and sufficient condition for problem solvability is established.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 229.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 299.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 299.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. van der Schaft, A., Schumacher, H.: An Introduction to Hybrid Dynamical Systems. Lecture Notes in Control and Information Sciences, vol. 251, Springer, London (2000)

    Google Scholar 

  2. Engell, S., Frehse, G., Schnieder, E.: Modeling, Analysis and Design of Hybrid Systems. Lecture Notes in Control and Information Sciences, vol. 279. Springer, Berlin (2002)

    Google Scholar 

  3. Savkin, A.V., Evans, R.J.: Hybrid Dynamical Systems. Controller and Sensor Switching Problems, Control Engineering Series, Birkhäuser, Boston (2002)

    Google Scholar 

  4. Haddad, W.M., Chellaboina, V.S., Nersesov, S.G.: Impulsive and Hybrid Dynamical Systems: Stability, Dissipativity, and Control, Princeton Series in Applied Mathematics, vol. 6. Princeton University Press, Princeton, NJ (2006)

    Google Scholar 

  5. Goebel, R., Sanfelice, R.G., Teel, A.R.: Hybrid Dynamical Systems: Modeling, Stability, and Robustness. Princeton University Press, Princeton, NJ (2012)

    Google Scholar 

  6. Djemai, M., Deefort, M.: Hybrid Dynamical Systems. Lecture Notes in Control and Information Sciences, vol. 457. Springer, Berlin (2015)

    Google Scholar 

  7. Liberzon, D.: Switching in Systems and Control. Systems and Control: Foundations and Applications. Birkhäuser, Boston, MA (2003)

    Google Scholar 

  8. Sun, Z., Ge, S.S.: Switched Linear Systems: Control and Design. Springer, New York (2005)

    Google Scholar 

  9. Sun, Z., Ge, S.S.: Stability Theory of Switched Dynamical Systems. Communications and Control Engineering. Springer, New York (2011)

    Google Scholar 

  10. Zhao, X., Kao, Y., Niu, B., Wu, T.: Control Synthesis of Switched Systems, Studies in Systems, Decision and Control, vol. 80. Springer, Cham, Switzerland (2017)

    Google Scholar 

  11. Fei, Z., Shi, S., Shi, P.: Analysis and Synthesis for Discrete-Time Switched Systems. A Quasi-Time-Dependent Method, Studies in Systems, Decision and Control, vol 244. Springer, Cham, Switzerland (2020)

    Google Scholar 

  12. Medina, E.A., Lawrence, D.A.: Controlled and conditioned invariants for linear impulsive systems. In: 45th IEEE Conference on Decision and Control, pp. 2753–2758. San Diego, CA (2006)

    Google Scholar 

  13. Carnevale, D., Galeani, S., Menini, L., Sassano, M.: Hybrid output regulation for linear systems with periodic jumps: Solvability conditions, structural implications and semi-classical solutions. IEEE Trans. Automat. Control 61(9), 2416–2431 (2016)

    Google Scholar 

  14. Zattoni, E., Perdon, A.M., Conte, G.: Output regulation by error dynamic feedback in hybrid systems with periodic state jumps. Automatica 81(7), 322–334 (2017)

    Google Scholar 

  15. Carnevale, D., Galeani, S., Menini, L., Sassano, M.: Robust hybrid output regulation for linear systems with periodic jumps: Semi-classical internal model design. IEEE Trans. Automat. Control 62(12), 6649–6656 (2017)

    Google Scholar 

  16. Zattoni, E., Perdon, A.M., Conte, G.: Measurement dynamic feedback output regulation in hybrid linear systems with state jumps. Int. J. Robust Nonlinear Control 28(2), 416–436 (2018)

    Google Scholar 

  17. Mattioni, M., Monaco, S., Normand-Cyrot, D.: On the zero-dynamics of a class of hybrid LTI systems: A geometric approach. IEEE Control Syst. Lett. 3(3), 703–708 (2019)

    Google Scholar 

  18. Galeani, S., Sassano, M.: Output regulation of hybrid linear systems: Solvability conditions and structural implications. In: Zattoni, E., Perdon, A.M., Conte, G. (eds.) Structural Methods in the Study of Complex Systems. Lecture Notes in Control and Information Sciences, vol. 482, pp. 115–151. Cham, Switzerland (2020)

    Google Scholar 

  19. De Carolis, G., Galeani, S., Sassano, M.: Robust hybrid output regulation for linear systems with periodic jumps: The non-semiclassical case. IEEE Control Syst. Lett. 4(1), 25–30 (2020)

    Google Scholar 

  20. Liu, Y., Zhao, J.: Output regulation of a class of switched linear systems with disturbances. In: 2001 American Control Conference, pp. 882–883. Arlington, VA (2001)

    Google Scholar 

  21. Lee, J.W., Khargonekar, P.P.: Detectability and stabilizability of discrete-time switched linear systems. IEEE Trans. Automat. Control 54(3), 424–437 (2009)

    Google Scholar 

  22. Lu, L.: Output regulation of a class of switched linear systems with saturated continuous feedback. In: 30th Chinese Control Conference, pp. 1819–1825. Yantai, China (2011)

    Google Scholar 

  23. Zattoni, E., Perdon, A.M., Conte, G.: A geometric approach to output regulation for linear switching systems. In: 5th IFAC Symposium on System Structure and Control, IFAC Proceedings Volumes (IFAC-PapersOnLine), vol. 46(2), pp. 172–177. Grenoble, France (2013a)

    Google Scholar 

  24. Zattoni, E., Perdon, A.M., Conte, G.: The output regulation problem with stability for linear switching systems: a geometric approach. Automatica 49(10), 2953–2962 (2013b)

    Google Scholar 

  25. Dong, X., Zhang, J.: Solvability of output regulation for cascade switched nonlinear systems. IEEE Access 5:18, 334–18, 342 (2017)

    Google Scholar 

  26. Zhao, Y., Ma, D., Zhao, J.: Almost output regulation bumpless transfer control for switched linear systems. IET Control Theory Appl. 12(14), 1932–1940 (2018)

    Google Scholar 

  27. Xie, J., Yang, D., Zhao, J.: Multiple model adaptive control for switched linear systems: A two-layer switching strategy. Int. J. Robust Nonlinear Control 28(6), 2276–2297 (2018)

    Google Scholar 

  28. Perdon, A.M., Zattoni, E., Conte, G.: Disturbance decoupling in hybrid linear systems with state jumps. IEEE Trans. Automat. Control 62(12), 6552–6559 (2017)

    Google Scholar 

  29. Cristofaro, A., Sassano, M.: The disturbance decoupling problem for hybrid systems with state-driven jumps. IFAC-PapersOnLine 50(1), 892–897 (2017)

    Google Scholar 

  30. Duz, A., Phillips, S., Fagiolini, A., Sanfelice, R., Pasqualetti, F.: Stealthy attacks in cloud-connected linear impulsive systems. In: American Control Conference, pp. 146–152 Milwaukee, WI (2018)

    Google Scholar 

  31. Zhu, B., Suo, M., Chen, L., Li, S.: Stability and \({L}_1\)-gain analysis for positive Takagi-Sugeno fuzzy systems with impulse. IEEE Trans. Fuzzy Syst. 26(6), 3893–3901 (2018)

    Google Scholar 

  32. Menini, L., Possieri, C., Tornambè, A.: Design of controllers for hybrid linear systems with impulsive inputs and periodic jumps. IET Control Theory Appl. 13(9), 1344–1354 (2019)

    Google Scholar 

  33. Zhu, B., Zhang, J., Suo, M., Chen, L., Zhang, Y., Li, S.: Robust stability analysis and controller synthesis for uncertain impulsive positive systems under \({L}_1\)-gain performance. ISA Trans. 93, 55–69 (2019).

    Google Scholar 

  34. Otsuka, N.: Disturbance decoupling with quadratic stability for switched linear systems. Syst. Control Lett. 59(6), 349–352 (2010)

    Google Scholar 

  35. Yurtseven, E., Heemels, W.P.M.H., Camlibel, M.K.: Disturbance decoupling of switched linear systems. Syst. Control Lett. 61(1), 69–78 (2012)

    Google Scholar 

  36. Zattoni, E., Perdon, A.M., Conte, G.: Disturbance decoupling with closed-loop modes stability in switched linear systems. IEEE Trans. Automat. Control 61(10), 3115–3121 (2016)

    Google Scholar 

  37. Everts, A.R.F., Camlibel, M.K.: When is a linear multi-modal system disturbance decoupled? Syst. Control Lett. 101, 50–57 (2017)

    Google Scholar 

  38. Kaldmäe, A., Kotta, U., Shumsky, A., Zhirabok, A.: Disturbance decoupling in nonlinear hybrid systems. Nonlinear Anal. Hybrid Syst. 28, 42–53 (2018)

    Google Scholar 

  39. Zhou, J., Serrani, A.: A stratified geometric approach to the disturbance decoupling problem with stability for switched systems over digraphs. In: Zattoni, E., Perdon, A.M., Conte, G. (eds.) Structural Methods in the Study of Complex Systems. Lecture Notes in Control and Information Sciences, vol. 482, pp. 153–165. Cham, Switzerland (2020)

    Google Scholar 

  40. Zattoni, E.: Structural model matching in hybrid linear systems with state jumps. In: American Control Conference, pp. 511–516. Seattle, WA (2017)

    Google Scholar 

  41. Zattoni, E.: A geometric approach to structural model matching by output feedback in linear impulsive systems. Int. J. Appl. Math. Comput. Sci. 28(1), 25–38 (2018). Invited paper in the special session “Issues in Parameter Identification and Control”, A. Aitouche Ed

    Google Scholar 

  42. Dong, Z., Tan, B., Zhang, Y., Yuan, J., Feng, E., Yin, H., Xiu, Z.: Strong stability of an optimal control hybrid system in fed-batch fermentation. Int. J. Biomath. 11(4) (2018)

    Google Scholar 

  43. Zattoni, E., Perdon, A.M., Conte, G.: Output-feedback model matching with strong stability for hybrid linear systems with periodic state jumps. In: 17th European Control Conference, pp. 441–446. Limassol, Cyprus (2018)

    Google Scholar 

  44. Conte, G., Perdon, A.M., Zattoni, E.: Asymptotic model matching for hybrid linear systems with state jumps. In: IEEE Conference on Decision and Control, pp. 2384–2389. Miami, FL (2018)

    Google Scholar 

  45. Jiang, S., Voulgaris, P.G.: Performance optimization of switched systems: A model matching approach. IEEE Trans. Automat. Control 54(9), 2058–2071 (2009)

    Google Scholar 

  46. Naghnaeian, M., Voulgaris, P.G.: On model matching problems of input-output switching systems. In: 51st IEEE Conference on Decision and Control, pp. 2643–2647. Maui, HI (2012)

    Google Scholar 

  47. Perdon, A.M., Conte, G., Zattoni, E.: Necessary and sufficient conditions for asymptotic model matching of switching linear systems. Automatica 64, 294–304 (2016a)

    Google Scholar 

  48. Perdon, A.M., Zattoni, E., Conte, G.: Model matching with strong stability in switched linear systems. Syst. Control Lett. 97, 98–107 (2016b)

    Google Scholar 

  49. Du, D., Xu, S., Cocquempot, V.: Actuator fault estimation for discrete-time switched systems with finite-frequency. Syst. Control Lett. 108, 64–70 (2017)

    Google Scholar 

  50. Pina, L., Botto, M.: Simultaneous state and input estimation of hybrid systems with unknown inputs. Automatica 42(5), 755–762 (2006)

    Google Scholar 

  51. Takrouni, A., Ksouri, M., Zanzouri, N., Cocquempot, V.: Mode recognition and fault detection of hybrid dynamical systems by unknown input observers. Int. Rev. Automat. Control 5(1), 49–55 (2012)

    Google Scholar 

  52. Conte G, Perdon AM, Zattoni E (2017) Unknown input observers for hybrid linear systems with state jumps. In: 20th IFAC World Congress, Toulouse, France; IFAC-PapersOnLine 50(1), 6458–6464

    Google Scholar 

  53. Conte, G., Perdon, A.M., Zattoni, E.: Unknown-input state observers with minimal order for linear impulsive systems. In: 18th European Control Conference, pp. 269–274. Italy, Napoli (2019)

    Google Scholar 

  54. Conte, G., Perdon, A.M., Zattoni, E.: Unknown-input state observers for hybrid dynamical structures. In: Zattoni, E., Perdon, A.M., Conte, G. (eds.) Structural Methods in the Study of Complex Systems. Lecture Notes in Control and Information Sciences, vol. 482, pp. 167–201. Cham, Switzerland (2020)

    Google Scholar 

  55. Pettersson, S.: Designing switched observers for switched systems using multiple Lyapunov functions and dwell-time switching. IFAC Proceedings Volumes (IFAC-PapersOnline) 2(PART 1), 18–23 (2006)

    Google Scholar 

  56. Bejarano, F.J., Pisano, A.: Switched observers for switched linear systems with unknown inputs. IEEE Trans. Automat. Control 56(3), 681–686 (2011)

    Google Scholar 

  57. Bejarano, F.J., Pisano, A., Usai, E.: Finite-time converging jump observer for switched linear systems with unknown inputs. Nonlinear Anal. Hybrid Syst. 5(2), 174–188 (2011)

    Google Scholar 

  58. Defoort, M., Van Gorp, J., Djemai, M., Veluvolu, K.: Hybrid observer for switched linear systems with unknown inputs. In: 7th IEEE Conference on Industrial Electronics and Applications, ICIEA 2012, pp. 594–599 (2012)

    Google Scholar 

  59. Conte, G., Perdon, A.M., Zattoni, E.: The unknown input observation problem for switching systems with dwell-time. In: 56th IEEE Conference on Decision and Control, pp. 3626–3633. Melbourne, Australia (2017)

    Google Scholar 

  60. Yang, J., Chen, Y., Wang, X.: Active mode identification and continuous state estimation for switched linear systems with unknown inputs and slow switching signal. Circuits Syst. Signal Process.34(7), 2193–2211 (2015)

    Google Scholar 

  61. Du, D., Cocquempot, V., Jiang, B.: Robust fault estimation observer design for switched systems with unknown input. Appl. Math. Comput. 348, 70–83 (2019)

    Google Scholar 

  62. Conte, G., Perdon, A.M., Zattoni, E.: A structural approach to unknown inputs observation for switching linear systems. Automatica 129(7), 1–12 (2021). https://doi.org/10.1016/j.automatica.2021.109572, article n. 109572

  63. Li, Z., Soh, Y., Wen, C.: Switched and Impulsive Systems: Analysis, Design and Applications. Lecture Notes in Control and Information Sciences, vol. 313. Springer, Berlin Heidelberg (2005)

    Google Scholar 

  64. Xie, G., Wang, L.: Necessary and sufficient conditions for controllability and observability of switched impulsive control systems. IEEE Trans. Automat. Control 49(6), 960–966 (2004)

    Google Scholar 

  65. Guan, Z.H., Hill, D.J., Shen, X.: On hybrid impulsive and switching systems and application to nonlinear control. IEEE Trans. Automat. Control 50(7), 1058–1062 (2005)

    Google Scholar 

  66. Xu, H., Liu, X., Teo, K.L.: A LMI approach to stability analysis and synthesis of impulsive switched systems with time delays. Nonlinear Anal. Hybrid Syst. 2(1), 38–50 (2008)

    Google Scholar 

  67. Ren, W., Xiong, J.: Vector-Lyapunov-function-based input-to-state stability of stochastic impulsive switched time-delay systems. IEEE Trans. Automat. Control 64(2), 654–669 (2019)

    Google Scholar 

  68. Gao, R., Liu, X., Yang, J.: On optimal control problems of a class of impulsive switching systems with terminal states constraints. Nonlinear Anal. Theory, Methods Appl. 73(7), 1940–1951 (2010)

    Google Scholar 

  69. Conte, G., Perdon, A.M., Zattoni, E.: Disturbance decoupling with stability for impulsive switching linear systems. In: 7th IFAC Symposium on System Structure and Control, Sinaia, Romania, IFAC PapersOnLine, 52(17), 19–24 (2019). https://doi.org/10.1016/j.ifacol.2019.11.20

  70. Zou, Q., Devasia, S.: Preview-based stable-inversion for output tracking of linear systems. J. Dyn. Syst. Meas. Control 121, 625–630 (1999)

    Google Scholar 

  71. Mirkin, L.: On the \({H}^\infty \) fixed-lag smoothing: how to exploit the information preview. Automatica 39(8), 1495–1504 (2003)

    Google Scholar 

  72. Marro, G., Prattichizzo, D., Zattoni, E.: A unified setting for decoupling with preview and fixed-lag smoothing in the geometric context. IEEE Trans. Automat. Control 51(5), 809–813 (2006)

    Google Scholar 

  73. Zattoni, E.: Decoupling of measurable signals via self-bounded controlled invariant subspaces: Minimal unassignable dynamics of feedforward units for prestabilized systems. IEEE Trans. Automat. Control 52(1), 140–143 (2007)

    Google Scholar 

  74. Morse, A.S.: Supervisory control of families of linear set-point controllers–Part I: Exact matching. IEEE Trans. Automat. Control 41(10), 1413–1431 (1996)

    Google Scholar 

  75. Liberzon, D., Hespanha, J.P., Morse, A.S.: Stability of switched systems: A Lie-algebraic condition. Syst. Control Lett. 37(3), 117–122 (1999)

    Google Scholar 

  76. Conte, G., Perdon, A.M., Zattoni, E.: The disturbance decoupling problem for jumping hybrid systems. In: 54th IEEE Conference on Decision and Control, pp. 1589–1594. Osaka, Japan (2015)

    Google Scholar 

  77. Wonham, W.M.: Linear Multivariable Control: A Geometric Approach, 3rd edn. Springer, New York (1985)

    Google Scholar 

  78. Zattoni, E.: Measurable disturbance rejection with stability in continuous-time switched linear systems under dwell-time switching. In: European Control Conference 2014, pp. 2242–2247. Strasbourg, France (2014)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Elena Zattoni .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2022 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Zattoni, E., Passarella, A., Perdon, A.M., Conte, G. (2022). Measurable Disturbance Decoupling for Impulsive Switching Linear Systems. In: Zattoni, E., Simani, S., Conte, G. (eds) 15th European Workshop on Advanced Control and Diagnosis (ACD 2019). ACD 2019 2018. Lecture Notes in Control and Information Sciences - Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-030-85318-1_10

Download citation

Publish with us

Policies and ethics