References

• 1. 1)
     • H. Lin , P.J. Anstaklis . Stability and stabilisability of switched linear systems: a survey of recent results. IEEE Trans. Autom. Control , 308 - 322
  2. 2)
     • 20. Pola, G., Bujorianu, M.L., Lygeros, J., Benedetto, M.D.D.: ‘Stochastic hybrid models: an overview with application to air traffic management’. Proc. IFAC Conf. on Analysis and Design of Hybrid Systems, June 2003, pp. 45–50.
  3. 3)
     • 38. Blanchini, F., Miani, S., Mesquine, F.: ‘A separation principle for linear switching systems and parameterization of all stabilizing controllers’, IEEE Trans. Autom. Control, 2009, 54, (2), pp. 279–292 (doi: 10.1109/TAC.2008.2010896).
  4. 4)
     • 32. Wong, E., Zakai, M.: ‘Riemann–Stieltjes approximations of stochastic integrals’, Z. Wahr. Verw. Geb., 1969, 12, pp. 87–97 (doi: 10.1007/BF00531642).
  5. 5)
     • 11. Caldwell, T.M., Murphey, T.D.: ‘Switching mode generation and optimal estimation with application to skid-steering’, Automatica, 2011, 47, (1), pp. 50–64 (doi: 10.1016/j.automatica.2010.10.010).
  6. 6)
     • S.M. Williams , R.G. Hoft . Adaptive frenquency domain control of PPM switched power line conditioner. IEEE Trans. Power. Electron. , 4 , 665 - 670
  7. 7)
     • 13. Xu, X.P., Antsaklis, P.J.: ‘A dynamic programming approach for optimal control of switched systems’. Proc. IEEE Conf. on Decision and Control, Sydney, Australia, December 2000, pp. 1822–1827.
  8. 8)
     • 26. Xiang, Z.R., Qiao, C.H., Mahmoud, M.S.: ‘Finite-time analysis and H∞ control for switched stochastic systems’, J. Franklin Inst., 2012, 349, (3), pp. 915–927 (doi: 10.1016/j.jfranklin.2011.10.021).
  9. 9)
     • 36. Stursberg, O., Engell, S.: ‘Optimal control of switched continuous systems using mixed-integer programming’. Proc. IFAC World Congress Automatic Control, Barcelona, Spain, July 2002, pp. 558–558.
  10. 10)
      • 22. Filipovic, V.: ‘Exponential stability of stochastic switched systems’, Trans. Inst. Meas. Control, 2009, 31, (2), pp. 205–212 (doi: 10.1177/0142331208094523).
  11. 11)
      • 19. Egerstedt, M., Wardi, Y., Axelsson, H.: ‘Transition-time optimization for switched-mode dynamical systems’, IEEE Trans. Autom. Control, 2006, 51, (1), pp. 110–115 (doi: 10.1109/TAC.2005.861711).
  12. 12)
      • 14. Xu, X.P., Antsaklis, P.J.: ‘Optimal control of switched systems via non-linear optimization based on direct differentiations of value functions’, Int. J. Control, 2002, 75, (16–17), pp. 1406–1426 (doi: 10.1080/0020717021000023825).
  13. 13)
      • 28. Zhang, W., Hu, J., Lian, J.: ‘Quadratic optimal control of switched linear stochastic systems’, Syst. Control Lett., 2010, 59, (11), pp. 736–744 (doi: 10.1016/j.sysconle.2010.08.010).
  14. 14)
      • 33. Sussmann, H.J.: ‘On the gap between deterministic and stochastic ordinary differential equations’, Ann. Prob., 1978, 60, pp. 19–41 (doi: 10.1214/aop/1176995608).
  15. 15)
      • J. Zhao , M.W. Spong . Hybrid control for global stabilization of the cart-pendulum system. Automatica , 12 , 1941 - 1951
  16. 16)
      • 27. Åström, K.J.: ‘Introduction to stochastic control theory’ (Academic Press, New York, 1970).
  17. 17)
      • 12. Xu, X.P., Antsaklis, P.J.: ‘Optimal control of switched systems: new results and open problems’. Proc. American Control Conf., Chicago, Illinois, June 2000, pp. 2683–2687.
  18. 18)
      • 25. Xiang, Z.R., Wang, R.H., Chen, Q.W.: ‘Robust reliable stabilization of stochastic switched nonlinear systems under asynchronous switching’, Appl. Math. Comput., 2011, 217, (19), pp. 7725–7736 (doi: 10.1016/j.amc.2011.02.076).
  19. 19)
      • 5. Long, L.J., Zhao, J.: ‘Robust stabilisation of non-triangular multi-input switched non-linear systems and its application to a continuously stirred tank reactor system’, IET Control Theory Appl., 2013, 7, (5), pp. 697–706 (doi: 10.1049/iet-cta.2012.0711).
  20. 20)
      • 35. Polak, E.: ‘Optimization algorithms and consistent approximations’ (Springer-Verlag Press’, New York, 1997).
  21. 21)
      • 37. Mahboubi, H., Moshiri, B., Khaki Seddigh, A.: ‘Hybrid modeling and optimal control of a two-tank system as a switched system’, World Acad. Sci. Eng. Tech., 2007, 1, (11), pp. 789–803.
  22. 22)
      • 21. Ghosh, M.K., Arapostathis, A., Marcus, S.I.: ‘Optimal control of switching diffusions with application to flexible manufacturing systems’, SIAM J. Control Optim., 1993, 31, (5), pp. 1183–1204 (doi: 10.1137/0331056).
  23. 23)
      • 2. Egerstedt, M., Hu, X.: ‘A hybrid control approach to action coordination for mobile robots’, Automatica, 2002, 38, (1), pp. 125–130 (doi: 10.1016/S0005-1098(01)00185-6).
  24. 24)
      • 31. Oksendal, B.: ‘Stochastic differential equations – an introduction with applications’ (Springer-Verlag, Berlin, 2003, 6th edn.).
  25. 25)
      • M.S. Branicky , V.S. Borkar , S.K. Mitter . A unified framework for hybrid control: model and optimal control theory. IEEE Trans. Autom. Control , 1 , 31 - 45
  26. 26)
      • 10. Le Ny, J., Feron, E., Pappas, G.J.: ‘Resource constrained LQR control under fast sampling’. Proc. Int. Conf. on Hybrid Systems: Computation and Control, Chicago, USA, April 2011, pp. 271–280.
  27. 27)
      • 34. Khasminskii, R.: ‘Stochastic stability of differential equations’ (Springer, 2012).
  28. 28)
      • 18. Ding, X.C., Wardi, Y., Egerstedt, M.: ‘On-line optimization of switched-mode dynamical systems’, IEEE Trans. Autom. Control, 2009, 54, (9), pp. 2266–2271 (doi: 10.1109/TAC.2009.2026864).
  29. 29)
      • L. Wu , D.W.C. Ho , C.W. Li . Stabilization and performance synthesis for switched stochastic systems. IET Control Theory Appl. , 10 , 1877 - 1888
  30. 30)
      • 3. Tomlin, C.J., Lygeros, J., Sastry, S.S.: ‘A game theoretic approach to controller design for hybrid systems’, Proc. IEEE, 2000, 88, (7), pp. 949–970 (doi: 10.1109/5.871303).
  31. 31)
      • 16. Xu, X.P., Antsaklis, P.J.: ‘Optimal control of switched autonomous systems’. Proc. IEEE Conf. on Decision and Control, Las Vegas, Nevada, USA, December 2002, pp. 4401–4406.
  32. 32)
      • 15. Xu, X.P., Antsaklis, P.J.: ‘An approach to switched systems optimal control based on parameterization of the switching instants’. Proc. Int. Federation of Automatic Control, Barcelona, Spain, July 2002, p. 308.
  33. 33)
      • 17. Egerstedt, M., Wardi, Y., Delmotte, F.: ‘Optimal control of switching times in switched dynamical systems’. Proc. IEEE Conf. on Decision Control, Maui, Hawaii, December 2003, pp. 2138–2143.
  34. 34)
      • 24. Yao, J., Su, Y.Q., Guo, Y.F., Zhang, J.Q.: ‘Exponential synchronisation of hybrid impulsive and switching dynamical networks with time delays’, IET Control Theory Appl., 2013, 7, (4), pp. 508–514 (doi: 10.1049/iet-cta.2012.0345).
  35. 35)
      • 30. Skafidas, E., Evans, R.J., Mareels, I.M.Y., Nerode, A.: ‘Optimal controller switching for stochastic systems’, Hybrid Syst. V, 1999, LNCS1567, pp. 341–355 (doi: 10.1007/3-540-49163-5_19).
  36. 36)
      • 8. Niu, B., Zhao, J.: ‘Robust H∞ control for a class of switched nonlinear systems with average dwell time’, Int. J. Control, 2013, 86, (6), pp. 1107–1117 (doi: 10.1080/00207179.2013.779750).
  37. 37)
      • 39. Majdoub, N., Sakly, A., Benrejeb, M.: ‘Hybrid approach compared to gradient method for optimal control problem of hydraulic system’, Int. J. Res. Rev. Appl. Sci., 2012, 10, (2), pp. 200–214.
  38. 38)
      • 9. Lee, J.W.: ‘Infinite-horizon joint LQG synthesis of switching and feedback in discrete time’, IEEE Trans. Autom. Control, 2009, 54, (8), pp. 1945–1951 (doi: 10.1109/TAC.2009.2023780).
  39. 39)
      • 29. Koutsoukos, X.D.: ‘Optimal control of stochastic hybrid systems based on locally consistent Markov decision processes’. Proc. IEEE Int. Symp. on Intelligent Control, Mediterrean Conf. on Control and Automation, Limassol, Cyprus, June 2005, pp. 435–440.