This paper addresses the controller synthesis problem of discrete-time switched positive systems with bounded time-varying delays. Based on the switched copositive Lyapunov function approach, some necessary and sufficient conditions for the existence of state-feedback controller are presented as a set of linear programming and linear matrix inequality problems, hence easy to be verified. Another advantage is that the state-feedback law is independent on time-varying delays and initial conditions. A numerical example is provided to illustrate the effectiveness and feasibility of the developed controller.<\/p>\r\n","references":"[1] A. Berman, M. Neumann, and R. Stern, Nonnegative matrices in dynamic\r\nsystems. Wiley, New York, 1989.\r\n[2] T. Kaczorek, Positive 1D and 2D Systems. Springer- Verlag, London,\r\n2002.\r\n[3] L. Benvenuti, A. D. Santis, and L. Farina, Positive Systems. Springer-\r\nVerlag, Berlin, Germany, 2003.\r\n[4] M. Bus\u253c\u00e9icz, T. Kaczorek, \"Robust stability of positive discrete-time\r\ninterval systems with time-delays,\" Bulletin of the Polish Academy of\r\nSciences, vol. 52(2), pp. 99-102, 2005.\r\n[5] R. Shorten, D. Leith, J. Foy, and R. Kilduff, \"Towards an analysis and\r\ndesign framework for congestion control in communication networks,\"\r\nProceedings of the 12th Yale Workshop on Adaptive and Learning\r\nSystems, Yale University, New Haven, CT, USA, 2003.\r\n[6] A. Jadbabaie, J. Lin, and A. Morse, \"Coordination of groups of mobile\r\nautonomous agents using nearest neighbor rules,\" IEEE Transaction on\r\nAutomatic Control, vol. 48(6), pp. 1099-1103, 2003.\r\n[7] T. Kaczorek, \"The choice of the forms of lyapunov functions for a positive\r\n2d roesser model,\" International Journal of Applied Mathematics and\r\nComputer Science, vol. 17(4), pp. 471- 475, 2007.\r\n[8] T. Kaczorek, \"A realzation problem for positive continuous-time systems\r\nwith reduced numbers of delays,\" International Journal of Applied\r\nMathematics and Computer Science. vol. 16(3), pp. 325-331, 2006.\r\n[9] M. Rami, F. Tadeo, and A. Benzaouia, \"Control of constrained positive\r\ndiscrete systems,\" Proceedings of the American Control Conference, New\r\nYork City, USA, pp. 5851-5857, 2007.\r\n[10] R. Shorten, F. Wirth, O. Mason, K. Wulff, and C. King, \"Stability theory\r\nfor switched and hybrid systems,\" Linear Algebra and its Application,\r\nvol. 49(4), pp. 545-592, 2007.\r\n[11] O. Mason, R. Shorten, \"A conjecture on the existence of common\r\nquadratic lyapunov functions for positive linear systems,\" Proceedings of\r\nthe American Control Conference, New York City, USA, pp. 4469-4470,\r\n2003.\r\n[12] L. Gurvits, R. Shorten, and O. Mason, \"On the stability of switched positive\r\nlinear systems,\" IEEE Transaction on Automatic Control vol. 52(6),\r\npp. 1099-1103, 2007.\r\n[13] O. Mason, R. Shorten, \"On the simultaneous diagonal stability of pair of\r\npositive linear systems,\" Linear Algebra and its Application, vol. 413(1),\r\npp. 13-23, 2006.\r\n[14] L. Farina, S. Rinaldi, Positive linear systems: theory and applications.\r\nWiley, New York, 2000.\r\n[15] O. Mason, R. Shorten, \"On linear copositive lyapunov functions and\r\nthe stability of switched positive linear systems,\" IEEE Transaction on\r\nAutomatic Control, vol. 52(7), pp. 1346-1349, 2007.\r\n[16] X. Liu, \"Stability analysis of switched positive systems: A switched linear\r\ncopositive lyapunov function method,\" IEEE Transaction on Circuits\r\nand Systtems II, vol. 56(5), pp. 414- 418, 2009.\r\n[17] X. Liu, \"Stability analysis of positive systems with bounded timevarying\r\ndelays,\" IEEE Transaction on Circuits and Systtems II, vol. 56(7),\r\npp. 600-604, 2009.\r\n[18] M. Vidyasagar, Nonlinear Systems Analysis. Prentice- Hall, Upper\r\nSaddle River, NJ, 1993.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 44, 2010"}