Advertisement

Introduction

  • Zhendong SunEmail author
  • Shuzhi Sam Ge
Chapter
  • 1.6k Downloads
Part of the Communications and Control Engineering book series (CCE)

Abstract

Chapter 1 briefly introduces the problem formations and the organization of the book. In particular, given a feasible set of switching signals, the concepts of stability and stabilizability are introduced, and the related problems of stability and stabilization are briefly formulated and discussed. Examples and simulations are provided to exhibit the primary features of the problems with various switching mechanisms.

References

  1. 2.
    Aguiar AP, Hespanha JP, Pascoal AM. Switched seesaw control for the stabilization of underactuated vehicles. Automatica. 2007;43(12):1997–2008. zbMATHCrossRefMathSciNetGoogle Scholar
  2. 20.
    Baotic M, Christophersen FJ, Morari M. Constrained optimal control of hybrid systems with a linear performance index. IEEE Trans Autom Control. 2006;51(12):1903–19. CrossRefMathSciNetGoogle Scholar
  3. 24.
    Bengea SC, DeCarlo RA. Optimal control of switching systems. Automatica. 2005;41(1):11–27. zbMATHCrossRefMathSciNetGoogle Scholar
  4. 49.
    Camlibel MK, Heemels WPMH, Schumacher JM. Algebraic necessary and sufficient conditions for the controllability of conewise linear systems. IEEE Trans Autom Control. 2008;53(3):762–74. CrossRefMathSciNetGoogle Scholar
  5. 52.
    Cardim R, Teixeira MCM, Assuncao E, Covacic MR. Variable-structure control design of switched systems with an application to a DC–DC power converter. IEEE Trans Ind Electron. 2009;56(9):3505–13. CrossRefGoogle Scholar
  6. 54.
    Cheng DZ, Guo L, Lin YD, Wang Y. Stabilization of switched linear systems. IEEE Trans Autom Control. 2005;50(5):661–6. CrossRefMathSciNetGoogle Scholar
  7. 55.
    Cheng DZ, Lin YD, Wang Y. Accessibility of switched linear systems. IEEE Trans Autom Control. 2006;51(9):1486–91. CrossRefMathSciNetGoogle Scholar
  8. 60.
    Daafouz J, Riedinger P, Iung C. Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach. IEEE Trans Autom Control. 2002;47(11):1883–7. CrossRefMathSciNetGoogle Scholar
  9. 65.
    De Jong H, Gouze J-L, Hernandez C, Page M, Sari T, Geiselmann J. Qualitative simulation of genetic regulatory networks using piecewise-linear models. Bull Math Biol. 2004;66:301–40. CrossRefMathSciNetGoogle Scholar
  10. 66.
    De Persis C, De Santis R, Morse AS. Switched nonlinear systems with state-dependent dwell-time. Syst Control Lett. 2003;50(4):291–302. zbMATHCrossRefGoogle Scholar
  11. 67.
    De Santis E, Di Benedetto MD, Pola G. A structural approach to detectability for a class of hybrid systems. Automatica. 2009;45(5):1202–6. zbMATHCrossRefMathSciNetGoogle Scholar
  12. 68.
    Drenick R, Shaw L. Optimal control of linear plants with random parameters. IEEE Trans Autom Control. 1964;9(3):236–44. CrossRefGoogle Scholar
  13. 86.
    Ge SS, Sun Z. Switched controllability via bumpless transfer input and constrained switching. IEEE Trans Autom Control. 2008;53(7):1702–6. CrossRefMathSciNetGoogle Scholar
  14. 88.
    Geromel JC, Colaneri P, Bolzern P. Dynamic output feedback control of switched linear systems. IEEE Trans Autom Control. 2008;53(3):720–33. CrossRefMathSciNetGoogle Scholar
  15. 91.
    Goebel R, Sanfelice RG, Teel AR. Hybrid dynamical systems. IEEE Control Syst Mag. 2009;29(2):28–93. CrossRefMathSciNetGoogle Scholar
  16. 97.
    Guo YQ, Wang YY, Xie LH, Zheng JC. Stability analysis and design of reset systems: theory and an application. Automatica. 2009;45(2):492–7. zbMATHCrossRefMathSciNetGoogle Scholar
  17. 98.
    Gurvits L. Stabilities and controllabilities of switched systems (with applications to the quantum systems). In: Proc 15th int symp math theory network syst; 2002. Google Scholar
  18. 104.
    Hespanha JP. Uniform stability of switched linear systems: extensions of LaSalle’s invariance principle. IEEE Trans Autom Control. 2004;49(4):470–82. CrossRefMathSciNetGoogle Scholar
  19. 105.
    Hespanha JP, Liberzon D, Angeli D, Sontag ED. Nonlinear norm-observability notions and stability of switched systems. IEEE Trans Autom Control. 2005;50(2):154–68. CrossRefMathSciNetGoogle Scholar
  20. 122.
    Ji ZJ, Wang L, Guo XX. Design of switching sequences for controllability realization of switched linear systems. Automatica. 2007;43(4):662–8. zbMATHCrossRefMathSciNetGoogle Scholar
  21. 123.
    Jiang SX, Voulgaris PG. Performance optimization of switched systems: a model matching approach. IEEE Trans Autom Control. 2009;54(9):2058–71. MathSciNetGoogle Scholar
  22. 141.
    Lee JW, Khargonekar PP. Optimal output regulation for discrete-time switched and Markovian jump linear systems. SIAM J Control Optim. 2008;47(1):40–72. zbMATHCrossRefMathSciNetGoogle Scholar
  23. 142.
    Lee JW, Khargonekar PP. Detectability and stabilizability of discrete-time switched linear systems. IEEE Trans Autom Control. 2009;54(3):424–37. MathSciNetGoogle Scholar
  24. 145.
    Li ZG, Soh YC, Wen CY. Switched and impulsive systems: analysis, design and applications. Berlin: Springer; 2005. zbMATHGoogle Scholar
  25. 146.
    Liberzon D. Switching in systems and control. Boston: Birkhäuser; 2003. zbMATHGoogle Scholar
  26. 147.
    Liberzon D, Hespanha JP, Morse AS. Stability of switched systems: a Lie-algebraic condition. Syst Control Lett. 1999;37(3):117–22. zbMATHCrossRefMathSciNetGoogle Scholar
  27. 151.
    Lin H, Antsaklis PJ. Stability and stabilizability of switched linear systems: a survey of recent results. IEEE Trans Autom Control. 2009;54(2):308–22. CrossRefMathSciNetGoogle Scholar
  28. 155.
    Lu L, Lin ZL. A switching anti-windup design using multiple Lyapunov functions. IEEE Trans Autom Control. 2010;55(1):142–8. MathSciNetGoogle Scholar
  29. 159.
    Mancilla-Aguilar JL, Garcia RA. A converse Lyapunov theorem for nonlinear switched systems. Syst Control Lett. 2000;41(1):67–71. zbMATHCrossRefMathSciNetGoogle Scholar
  30. 161.
    Margaliot M. Stability analysis of switched systems using variational principles: an introduction. Automatica. 2006;42(12):2059–77. zbMATHCrossRefMathSciNetGoogle Scholar
  31. 164.
    Margaliot M, Liberzon D. Lie-algebraic stability conditions for nonlinear switched systems and differential inclusions. Syst Control Lett. 2006;55(1):8–16. zbMATHCrossRefMathSciNetGoogle Scholar
  32. 180.
    Morse AS. Lecture notes on logically switched dynamical systems. In: Agrachev AA, Morse AS, Sontag ED, Sussmann HJ, Utkin VI, editors. Nonlinear and optimal control theory. Berlin: Springer; 2008. p. 61–161. CrossRefGoogle Scholar
  33. 186.
    Oktem H. A survey on piecewise-linear models of regulatory dynamical systems. Nonlinear Anal. 2005;63(3):336–49. CrossRefMathSciNetGoogle Scholar
  34. 200.
    Santarelli KR, Dahleh MA. Optimal controller synthesis for a class of LTI systems via switched feedback. Syst Control Lett. 2010;59(3–4):258–64. zbMATHCrossRefMathSciNetGoogle Scholar
  35. 201.
    Seatzu C, Corona D, Giua A, Bemporad A. Optimal control of continuous-time switched affine systems. IEEE Trans Autom Control. 2006;51(5):726–41. CrossRefMathSciNetGoogle Scholar
  36. 208.
    Shorten RN, Wirth F, Mason O, Wulff K, King C. Stability criteria for switched and hybrid systems. SIAM Rev. 2007;49(4):545–92. zbMATHCrossRefMathSciNetGoogle Scholar
  37. 209.
    Solmaz S, Shorten RN, Wulff K, Cairbre F. A design methodology for switched discrete time linear systems with applications to automotive roll dynamics control. Automatica. 2008;44(9):2358–63. zbMATHCrossRefMathSciNetGoogle Scholar
  38. 216.
    Sun Z. Stabilizability and insensitiveness of switched systems. IEEE Trans Autom Control. 2004;49(7):1133–7. CrossRefGoogle Scholar
  39. 219.
    Sun Z. Combined stabilizing strategies for switched linear systems. IEEE Trans Autom Control. 2006;51(4):666–74. CrossRefGoogle Scholar
  40. 220.
    Sun Z. Stabilization and optimal switching of switched linear systems. Automatica. 2006;42(5):783–8. zbMATHCrossRefMathSciNetGoogle Scholar
  41. 225.
    Sun Z. Stabilizing switching design for switched linear systems: a state-feedback path-wise switching approach. Automatica. 2009;45(7):1708–14. zbMATHCrossRefGoogle Scholar
  42. 227.
    Sun Z. The problem of slow switching for switched linear systems. In: Proc ICCAS-SICE; 2009. p. 4843–6. Google Scholar
  43. 232.
    Sun Z, Ge SS. Dynamic output feedback stabilization of a class of switched linear systems. IEEE Trans Circuits Syst I, Fundam Theory Appl. 2003;50(8):1111–5. CrossRefMathSciNetGoogle Scholar
  44. 233.
    Sun Z, Ge SS. Analysis and synthesis of switched linear control systems. Automatica. 2005;41(2):181–95. zbMATHCrossRefMathSciNetGoogle Scholar
  45. 234.
    Sun Z, Ge SS. Switched linear systems: control and design. London: Springer; 2005. zbMATHGoogle Scholar
  46. 235.
    Sun Z, Ge SS. On stability of switched linear systems with perturbed switching paths. J Control Theory Appl. 2006;4(1):18–25. zbMATHCrossRefMathSciNetGoogle Scholar
  47. 236.
    Sun Z, Ge SS, Lee TH. Reachability and controllability criteria for switched linear systems. Automatica. 2002;38(5):775–86. zbMATHCrossRefMathSciNetGoogle Scholar
  48. 240.
    Sworder D. Control of a linear system with a Markov property. IEEE Trans Autom Control. 1965;10(3):294–300. CrossRefMathSciNetGoogle Scholar
  49. 241.
    Sworder D. Feedback control of a class of linear systems with jump parameters. IEEE Trans Autom Control. 1969;14(1):9–14. CrossRefMathSciNetGoogle Scholar
  50. 245.
    AH Tan. Direction-dependent systems—a survey. Automatica. 2009;45(12):2729–43. CrossRefGoogle Scholar
  51. 246.
    Tan PV, Millerioux G, Daafouz J. Left invertibility, flatness and identifiability of switched linear dynamical systems: a framework for cryptographic applications. Int J Control. 2010;83(1):145–53. zbMATHCrossRefGoogle Scholar
  52. 259.
    Wicks MA, Peleties P, DeCarlo RA. Switched controller synthesis for the quadratic stabilization of a pair of unstable linear systems. Eur J Control. 1998;4(2):140–7. zbMATHGoogle Scholar
  53. 261.
    Wirth F. A converse Lyapunov theorem for linear parameter-varying and linear switching systems. SIAM J Control Optim. 2005;44(1):210–39. zbMATHCrossRefMathSciNetGoogle Scholar
  54. 262.
    Witsenhausen HS. A class of hybrid-state continuous-time dynamic systems. IEEE Trans Autom Control. 1966;11(2):161–7. CrossRefGoogle Scholar
  55. 263.
    Wu AG, Feng G, Duan GR, Gao HJ. A stabilizing slow-switching law for switched discrete-time linear systems. In: Proc IEEE MSC; 2010. p. 2099–104. Google Scholar
  56. 266.
    Xie G, Wang L. Controllability and stabilizability of switched linear-systems. Syst Control Lett. 2003;48(2):135–55. zbMATHCrossRefMathSciNetGoogle Scholar
  57. 270.
    Xu X, Antsaklis PJ. Optimal control of switched systems based on parameterization of the switching instants. IEEE Trans Autom Control. 2004;49(1):2–16. CrossRefMathSciNetGoogle Scholar
  58. 279.
    Zhang W, Abate A, Hu JH, Vitus MP. Exponential stabilization of discrete-time switched linear systems. Automatica. 2009;45(11):2526–36. zbMATHCrossRefGoogle Scholar
  59. 281.
    Zhao J, Hill DJ. Dissipativity theory for switched systems. IEEE Trans Autom Control. 2008;53(4):941–53. CrossRefMathSciNetGoogle Scholar
  60. 283.
    Zhao J, Hill DJ, Liu T. Synchronization of complex dynamical networks with switching topology: a switched system point of view. Automatica. 2009;45(11):2502–11. zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.College Automation Science & Engineering, Center for Control and OptimizationSouth China University of TechnologyGuangzhouPeople’s Republic of China
  2. 2.Department of Electrical and Computer EngineeringThe National University of SingaporeSingaporeSingapore
  3. 3.Robotics Institue and Institute of Intelligent Systems and Information TechnologyUniversity of Electronic Science and Technology of ChinaChengduPeople’s Republic of China

Personalised recommendations