On the output controllability of positive discrete linear delay systems. (English) Zbl 1470.93027

Naim, Mouhcine; Lahmidi, Fouad; Namir, Abdelwahed; Rachik, Mostafa

Abstr. Appl. Anal. 2017, Article ID 3651271, 12 p. (2017).

Summary: Necessary and sufficient conditions for output reachability and null output controllability of positive linear discrete systems with delays in state, input, and output are established. It is also shown that output reachability and null output controllability together imply output controllability.

MSC:

93B05	Controllability
93C55	Discrete-time control/observation systems

References:

[1]	Kalman, R. E., On the general theory of control systems, Proceeding of the First International Congress on Automatic Control
[2]	Chen, C. T., Introduction to Linear System Theory, (1970), NY, USA: Holt, Rinehart and Winston, NY, USA
[3]	Klamka, J., Controllability of dynamical systems, 48, (1991), Dordrecht, The Netherlands: Kluwer Academic Publishers, Dordrecht, The Netherlands · Zbl 0732.93008
[4]	Klamka, J., Controllability of dynamical systems. A survey, Bulletin of the Polish Academy of Sciences: Technical Sciences, 61, 2, 335-342, (2013)
[5]	Bacciotti, A.; Mazzi, L., Asymptotic controllability by means of eventually periodic switching rules, SIAM Journal on Control and Optimization, 49, 2, 476-497, (2011) · Zbl 1217.93028 · doi:10.1137/100798260
[6]	Balachandran, K.; Kokila, J.; Trujillo, J. J., Relative controllability of fractional dynamical systems with multiple delays in control, Computers & Mathematics with Applications, 64, 10, 3037-3045, (2012) · Zbl 1268.93021 · doi:10.1016/j.camwa.2012.01.071
[7]	Klamka, J., Constrained controllability of second order dynamical systems with delay, Control and Cybernetics, 42, 1, 111-121, (2013) · Zbl 1318.93019
[8]	Shen, L.; Shi, J.; Sun, J., Complete controllability of impulsive stochastic integro-differential systems, Automatica, 46, 6, 1068-1073, (2010) · Zbl 1192.93021 · doi:10.1016/j.automatica.2010.03.002
[9]	Shen, L.; Sun, J., Approximate controllability of stochastic impulsive functional systems with infinite delay, Automatica, 48, 10, 2705-2709, (2012) · Zbl 1271.93025 · doi:10.1016/j.automatica.2012.06.098
[10]	Tie, L., On small-controllability and controllability of a class of nonlinear systems, International Journal of Control, 87, 10, 2167-2175, (2014) · Zbl 1308.93045 · doi:10.1080/00207179.2014.903565
[11]	Babiarz, A.; Czornik, A.; Niezabitowski, M., Output controllability of the discrete-time linear switched systems, Nonlinear Analysis: Hybrid Systems, 21, 1-10, (2016) · Zbl 1338.93068 · doi:10.1016/j.nahs.2015.12.004
[12]	Garca-Planas, M. I.; Domnguez-Garca, J. L., Alternative tests for functional and pointwise output-controllability of linear time-invariant systems, Systems & Control Letters, 62, 5, 382-387, (2013) · Zbl 1276.93016
[13]	Lau, D.; Oetomo, D.; Halgamuge, S. K., Generalized modeling of multilink cable-driven manipulators with arbitrary routing using the cable-routing matrix, IEEE Transactions on Robotics, 29, 5, 1102-1113, (2013) · doi:10.1109/TRO.2013.2264866
[14]	Domnguez-Garca, J. L.; Garca-Planas, M. I., Functional output-controllability analysis of fixed speed wind turbine, Proceedings of the 6th International Conference on Physics and Control
[15]	Garcia-Planas, M. I.; Tarragona, S., Analysis of functional output controllability of time-invariant composite linear systems, Recent Advances in Systems, Control and Informatics, 40-47, (2013)
[16]	Luenberger, D. G., Introduction to Dynamic Systems: Theory, Models and Applications, (1979), New York, NY, USA: Academic Press, New York, NY, USA · Zbl 0458.93001
[17]	Farina, L.; Rinaldi, S., Positive Linear Systems: Theory and Applications, (2000), New York, NY, USA: John Wiley, New York, NY, USA · Zbl 0988.93002 · doi:10.1002/9781118033029
[18]	Kaczorek, T., Positive 1D and 2D systems, Communications and Control Engineering, (2002), London, UK: Springer-Verlag, London, UK · Zbl 1005.68175
[19]	Briat, C., Dwell-time stability and stabilization conditions for linear positive impulsive and switched systems, Nonlinear Analysis: Hybrid Systems, 24, 198-226, (2017) · Zbl 1377.93127 · doi:10.1016/j.nahs.2017.01.004
[20]	Shen, J.; Lam, J., On l_{∞} and L_{∞} gains for positive systems with bounded time-varying delays, International Journal of Systems Science, 46, 1-8, (2015)
[21]	Coxson, P. G.; Shapiro, H., Positive input reachability and controllability of positive systems, Linear Algebra and its Applications, 94, 35-53, (1987) · Zbl 0633.93008 · doi:10.1016/0024-3795(87)90076-0
[22]	Fanti, M. P.; Maione, B.; Turchiano, B., Controllability of multi-input positive discrete-time systems, International Journal of Control, 51, 6, 1295-1308, (1990) · Zbl 0702.93012 · doi:10.1080/00207179008934134
[23]	Murthy, D. N. P., Controllability of a linear positive dynamic system, International Journal of Systems Science, 17, 1, 49-54, (1986) · Zbl 0581.93010 · doi:10.1080/00207728608926782
[24]	Rumchev, V. G.; James, D. J., Controllability of positive linear discrete-time systems, International Journal of Control, 50, 3, 845-857, (1989) · Zbl 0695.93009 · doi:10.1080/00207178908953401
[25]	Caccetta, L.; Rumchev, V. G., A survey of reachability and controllability for positive linear systems, Annals of Operations Research, 98, 101-122, (2000) · Zbl 0963.00033 · doi:10.1023/A:1019244121533
[26]	Valcher, M. E., Controllability and reachability criteria for discrete time positive systems, International Journal of Control, 65, 3, 511-536, (1996) · Zbl 0873.93009 · doi:10.1080/00207179608921708
[27]	Xie, G.; Wang, L.; Benvenuti, L.; De Santis, A.; Farina, L., Reachability and controllability of positive linear discrete-time systems with time-delays, Positive systems (Rome, 2003), 294, 377-384, (2003), Berlin, Germany: Springer, Berlin, Germany · Zbl 1067.93006
[28]	Kaczorek, T., Output-reachability of positive linear discrete-time systems, Proceeding of 7th International Workshop, Computational Problems of Electrical Engineering, (CPEE ’06), 64-68, (2006), Odessa, Ukraine
[29]	Kaczorek, T., Output-reachability of positive linear discrete-time systems with delays, Archives of Control Sciences, 16, 3, 247-255, (2006) · Zbl 1147.93310
[30]	Berman, A.; Plemmons, R. J., Nonnegative Matrices in the Mathematical Sciences, 9, (1994), Philadelphia, Pa, USA: Society for Industrial and Applied Mathematics, Philadelphia, Pa, USA · Zbl 0815.15016 · doi:10.1137/1.9781611971262
[31]	Buslowicz, M., On some properties of the solution of state equation of discrete-time systems with delays, Zesz. Nauk. Polit. Bial., Elektrotechnika, 1, 17-29, (1983)