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Research Article

On the positivity, excitability and transparency properties of a class of time-varying bilinear dynamic systems under multiple point internal and external delays

ORCID Icon | (Reviewing Editor)
Article: 1445409 | Received 25 Sep 2017, Accepted 13 Feb 2018, Published online: 09 Mar 2018

References

  • Al-Omari, J. F. M. (2015). The effect of state dependent delay and harvesting on a stage-structured predator-prey model. Applied Mathematics and Computation, 271, 142–153.10.1016/j.amc.2015.08.119
  • De la Sen, M. (1983). Application of the non-periodic sampling to the identifiability and model matching problems in dynamic systems. International Journal of Systems Science, 14(4), 367–383.10.1080/00207728308926464
  • De La Sen, M. (2002). Preserving positive realness through discretization. Positivity, 6(1), 31–45.10.1023/A:1012071600240
  • De La Sen, M. (2004). Sufficiency-type stability and stabilization criteria for linear time-invariant systems with constant point delays. Acta Applicandae Mathematicae, 83(3), 235–256.10.1023/B:ACAP.0000039018.13226.ed
  • De la Sen, M. (2007). About the positivity of a class of hybrid dynamic linear systems. Applied Mathematics and Computation, 189(1), 852–868.10.1016/j.amc.2006.11.182
  • De la Sen, M. (2008a). The generalized Beverton-Holt equation and the control of populations. Applied Mathematical Modelling, 32(11), 2312–2328.10.1016/j.apm.2007.09.007
  • De la Sen, M. (2008b). About the properties of excitability and transparency in positive systems with point delays. Applied Mathematical Modelling, 32(1), 40–60.10.1016/j.apm.2006.10.029
  • De la Sen, M., Agarwal, R. P., Ibeas, A., & Alonso-Quesada, S. (2011). On the existence of equilibrium points, boundedness, oscillating behavior and positivity of a SVEIRS epidemic model under constant and impulsive vaccination. Advances in Difference Equations, Article ID 748608. doi:10.1155/20117748608
  • De la Sen, M., & Ibeas, A. (2008). Stability results for switched linear systems with constant discrete delays. Mathematical Problems in Engineering, 2008, 28 pages, Article ID 543145. doi:10.1155/2008/543145
  • De la Sen, M., Paz, M. B., & Luo, N. (1998). Sensitivity identification and compensation in linear systems using nonperiodic sampling. Control and Intelligent Systems, 26(2), 50–66.
  • Domoshnitsky, A., & Volinsky, I. (2015). About differential inequalities for nonlocal boundary value problems with impulsive delay equations. Mathematica Bohemica, 140(2), 121–128.
  • Ebihara, Y. (2015). Analysis and synthesis of delay interconnected positive systems with external inputs and formation control of moving objects. In 2015 54th IEEE Conference on Decision and Control (CDC) (pp. 6367–6372). IEEE.10.1109/CDC.2015.7403222
  • Farina, S., & Rinaldi, R. (2000). Positive linear systems, theory and applications. New York, NY: Wiley-Interscience.10.1002/9781118033029
  • Feng, G., Chen, C. L., Sun, C. L., & Zhu, Y. (2005). H- infinity controller synthesis of fuzzy dynamic systems based on piecewise Lyapunov functions and bilinear matrix inequalities. IEEE Transactions on Fuzzy Systems, 13(1), 94–103.10.1109/TFUZZ.2004.839662
  • Goka, T., Tarn, T. J., & Zaborszky, J. (1973). On the controllability of a class of discrete bilinear systems. Automatica, 9(5), 615–622.10.1016/0005-1098(73)90046-0
  • Haldar, S., Chakraborty, K., & Kar, T. K. (2015). Controllability of an eco-epidemiological system with disease transmission delay: A theoretical study. Applications & Applied Mathematics, 10(1), 382–420.
  • Ibeas, A., De La Sen, M., & Alonso-Quesada, S. (2004). Stable multi-estimation model for single-input single-output discrete adaptive control systems. International Journal of Systems Science, 35(8), 479–501.10.1080/00207720412331280918
  • Kaczorek, T. (2001). Positive 1D and 2D Systems. In E. D. Sontag & M. Thoma (Eds.), Communications and control engineering series (431 pp.). Berlin: Springer-Verlag.
  • Kao, C. Y. (2014). On output feedback control of positive linear systems (pp. 881–885). SICE Annual Conference 2014, Hokkaido University, Japan.
  • Kittaneh, F. (2004). Norm inequalities for sums and differences of positive operators. Linear Algebra and its Applications, 383, 85–91.10.1016/j.laa.2003.11.023
  • Liao, W., Cannon, M., & Kouvaritakis, B. (2005). Constrained MPC using feedback linearization on SISO bilinear systems with unstable inverse dynamics. International Journal of Control, 78(9), 638–646.10.1080/00207170500118858
  • Mailleret, L. (2004). Stabilisation Globale des Systèmes Dynamiques Positifs Mal Connus. Applications in Biology, Écologie, Environnement. Université Nice Sophia Antipolis.
  • McCluskey, C., Conell, C., & Yang, Y. (2015). Global stability of a diffusive virus dynamics model with general incidence function and time delay. Nonlinear Analysis: Real World Applications, 25, 64–78.10.1016/j.nonrwa.2015.03.002
  • Monteiro, L. H. A., Gonçalves, C. H. O., & Piqueira, J. R. C. (2000). A condition for successful escape of a mutant after primary HIV infection. Journal of Theoretical Biology, 203(4), 399–406.10.1006/jtbi.2000.1092
  • Nalbant, N., Sozen, Y., Simos, T. E., Psihoyios, G., Sitouras, C., & Anastasi, Z. (2012). The positivity of differential operator with nonlocal boundary conditions. AIP Conference Proceedings-American Institute of Physics, 1479(1), 578.10.1063/1.4756198
  • Nickel, G., & Rhandi, A. (2005). Positivity and stability of delay equations with nonautonomous past. Mathematische Nachrichten, 278(7–8), 864–876.10.1002/(ISSN)1522-2616
  • Sau, N. H., Niamsup, P., & Phat, V. N. (2016). Positivity and stability analysis for linear implicit difference delay equations. Linear Algebra and its Applications, 510, 25–41.10.1016/j.laa.2016.08.012
  • Shenand, J., & Zheng, W. X. (2015). Positivity and stability of coupled differential–difference equations with time-varying delays. Automatica, 57, 123–127.
  • Stevic, S. (2006). A short proof of the Cushing- Henson conjecture. Discrete Dynamics in Nature and Society, 2006, 5 pages, Article ID 37264. doi:10.1155/2006/37264
  • Tarn, T. J. (1972). Singular control of bilinear discrete systems. Information and Control, 21, 211–234.10.1016/S0019-9958(72)80004-4
  • Tingting, L., Baowei, W., & Yunxu, T. (2015). Exponential stability of discrete-time linear singular positive time-delay systems. In The 27th Chinese Control and Decision Conference-2015 CCDC (pp. 6069–6073). Wuhan.
  • Yagi, A., & Ton, T. V. (2011). Dynamic of stochastic predator-prey population. Applied Mathematics and Computation, 218(7), 3100–3109.10.1016/j.amc.2011.08.037
  • Yi, S., Ulsoy, G., & Nelson, P. W. (2006). Solution of systems of linear delay differential equations via Laplace transformation. In Proceedings of the 45th IEEE Conference on Decision & Control (pp. 235–240). San Diego, CA.
  • Zames, G. (1966). On the input-output stability of time-varying nonlinear feedback systems. Part I: Conditions derived using concepts of loop gain, conicity and positivity, IEEE Transactions on Automatic Control, AC- 11(2), 228–238.