Exponential stability for discrete-time impulsive positive singular system with time delays

References

• Akhmet, M. U., Beklioglu, M., Ergenc, T., & Tkachenko, V. I. (2006). An impulsive ratio-dependent predator–prey system with diffusion. Nonlinear Analysis: Real World Applications, 7(5), 1255–1267.
   Web of Science ®Google Scholar
• Berman, A., & Plemmons, R. J. (1994). Nonnegative matrices in the mathematical sciences. SIAM.
   Google Scholar
• Briat, C (2013). Robust stability and stabilization of uncertain linear positive systems via integral linear constraints: L1−gain and L∞−gain characterization. International Journal of Robust and Nonlinear Control, 23(17), 1932–1954. https://doi.org/10.1002/rnc.v23.17
   Web of Science ®Google Scholar
• Briat, C. (2017). Dwell-time stability and stabilization conditions for linear positive impulsive and switched systems. Nonlinear Analysis: Hybrid Systems, 24, 198–226.
   Web of Science ®Google Scholar
• Cacace, F., Farina, L., Setola, R., & Germani, A. (2016). Positive systems: Theory and applications. Vol 471. Springer.
   Google Scholar
• Chellaboina, V., Bhat, S. P., Haddad, W. M., & Bernstein, D. S. (2009). Modeling and analysis of mass-action kinetics. IEEE Control Systems Magazine, 29(4), 60–78. https://doi.org/10.1109/MCS.2009.932926
   Web of Science ®Google Scholar
• Chen, W. H., Zheng, W. X., & Lu, X. (2017). Impulsive stabilization of a class of singular systems with time-delays. Automatica, 83, 28–36. https://doi.org/10.1016/j.automatica.2017.05.008
   Web of Science ®Google Scholar
• Chen, Y., Bo, Y., & Du, B. (2019). Positive L1-filter design for continuous-time positive Markov jump linear systems: Full-order and reduced-order. IET Control Theory & Applications, 13(12), 1855–1862. https://doi.org/10.1049/cth2.v13.12
   Web of Science ®Google Scholar
• Cui, Y., Shen, J., Feng, Z., & Chen, Y. (2017). Stability analysis for positive singular systems with time-varying delays. IEEE Transactions on Automatic Control, 63(5), 1487–1494. https://doi.org/10.1109/TAC.9
   Web of Science ®Google Scholar
• Dashkovskiy, S., & Mironchenko, A. (2013). Input-to-state stability of nonlinear impulsive system. SIAM Journal on Control and Optimization, 51(3), 1962–1987. https://doi.org/10.1137/120881993
   Web of Science ®Google Scholar
• Farina, L., & Rinaldi, S. (2000). Positive linear systems. Wiley.
   Google Scholar
• Feng, G., & Cao, J. (2015). Stability analysis of impulsive switched singular systems. IET Control Theory & Applications, 9(6), 863–870. https://doi.org/10.1049/cth2.v9.6
   Web of Science ®Google Scholar
• Feng, Z., Yang, Y., & Lam, H. K. (2021). Extended-dissipativity-based adaptive event-triggered control for stochastic polynomial fuzzy singular systems. IEEE Transactions on Fuzzy Systems, 30(8), 3224–3236. https://doi.org/10.1109/TFUZZ.2021.3107753
   Web of Science ®Google Scholar
• Hien, L. V., Trinh, H. M., & Pathirana, P. N. (2020). On l1−gain control of 2−D positive Roesser systems with directional delays: Necessary and sufficient conditions. Automatica, 112, 108720. https://doi.org/10.1016/j.automatica.2019.108720
   Web of Science ®Google Scholar
• Hu, M., Xiao, J., Xiao, X., & Chen, W. (2017). Impulsive effects on the stability and stabilization of positive systems with delays. Journal of the Franklin Institute, 354(10), 4034–4054. https://doi.org/10.1016/j.jfranklin.2017.03.019
   Web of Science ®Google Scholar
• Jiao, T., Zheng, W. X., & Xu, S. (2017). Stability analysis for a class of random nonlinear impulsive systems. International Journal of Robust and Nonlinear Control, 27(7), 1171–1193. https://doi.org/10.1002/rnc.v27.7
   Web of Science ®Google Scholar
• Leslie, P. H. (1945). On the use of matrices in certain population mathematics. Biometrika, 33(3), 183–212. https://doi.org/10.1093/biomet/33.3.183
   PubMed Web of Science ®Google Scholar
• Li, R., & Yang, Y. (2020). Fault detection for TS fuzzy singular systems via integral sliding modes. Journal of the Franklin Institute, 357(17), 13125–13143. https://doi.org/10.1016/j.jfranklin.2020.09.014
   Web of Science ®Google Scholar
• Li, X., Peng, D., & Cao, J. (2020). Lyapunov stability for impulsive systems via event-triggered impulsive control. IEEE Transactions on Automatic Control, 65(11), 4908–4913. https://doi.org/10.1109/TAC.9
   Web of Science ®Google Scholar
• Li, Y., & He, Y. (2021). New insight into admissibility analysis for singular systems with time-varying delays. International Journal of Systems Science, 52(13), 2752–2762. https://doi.org/10.1080/00207721.2021.1902016
   Web of Science ®Google Scholar
• Liu, B. (2008). Stability of solutions for stochastic impulsive systems via comparison approach. IEEE Transactions on Automatic Control, 53(9), 2128–2133. https://doi.org/10.1109/TAC.2008.930185
   Web of Science ®Google Scholar
• Liu, L., Xing, H., Cao, X., Fu, Z., & Song, S. (2018). Guaranteed cost finite-time control of discrete-time positive impulsive switched systems. Complexity, 2018, 1–8. https://doi.org/10.1155/2018/5790681
   Google Scholar
• Liu, X. (1994). Stability results for impulsive differential systems with applications to population growth models. Dynamics and Stability of Systems, 9(2), 163–174. https://doi.org/10.1080/02681119408806175
   Web of Science ®Google Scholar
• Liu, X., Yu, W., & Wang, L. (2009). Stability analysis of positive systems with bounded time-varying delays. IEEE Transactions on Circuits and Systems Part II: Express Briefs, 56(7), 600–604. https://doi.org/10.1109/tcsii.2009.2023305
   Web of Science ®Google Scholar
• Liu, X., Yu, W., & Wang, L. (2010). Stability analysis for continuous-time positive systems with time-varying delays. IEEE Transactions on Automatic Control, 55(4), 1024–1028. https://doi.org/10.1109/TAC.2010.2041982
   Web of Science ®Google Scholar
• Naghshtabrizi, P., Hespanha, J. P., & Teel, A. R. (2008). Exponential stability of impulsive systems with application to uncertain sampled-data systems. Systems & Control Letters, 57(5), 378–385. https://doi.org/10.1016/j.sysconle.2007.10.009
   Web of Science ®Google Scholar
• Nam, P. T., Pathirana, P. N., & Trinh, H. (2016). Partial state bounding with a pre-specified time of non-linear discrete systems with time-varying delays. IET Control Theory & Applications, 10(13), 1496–1502. https://doi.org/10.1049/cth2.v10.13
   Web of Science ®Google Scholar
• Phat, V. N., & Sau, N. H. (2018). Exponential stabilisation of positive singular linear discrete-time delay systems with bounded control. IET Control Theory & Applications, 13(7), 905–911. https://doi.org/10.1049/cth2.v13.7
   Web of Science ®Google Scholar
• Ren, Y., Er, M. J., & Sun, G. (2017). Asynchronous l1 positive filter design for switched positive systems with overlapped detection delay. IET Control Theory & Applications, 11(3), 319–328. https://doi.org/10.1049/cth2.v11.3
   Web of Science ®Google Scholar
• Sau, N. H., & Phat, V. N. (2018). LP approach to exponential stabilization of singular linear positive time-delay systems via memory state feedback. Journal of Industrial & Management Optimization, 14(2), 583–596. https://doi.org/10.3934/jimo.2017061
   Web of Science ®Google Scholar
• Sau, N. H., & Thuan, M. V. (2023). Impulsive stability for positive linear differential-algebraic equations with time-varying delay. IEEE Transactions on Automatic Control. https://doi.org/10.1109/TAC.2023.3250351.
   Google Scholar
• Shampine, L. F., & Gahinet, P. (2006). Delay-differential-algebraic equations in control theory. Applied Numerical Mathematics, 56(3-4), 574–588. https://doi.org/10.1016/j.apnum.2005.04.025
   Web of Science ®Google Scholar
• Smith, R. J., & Wahl, L. M. (2005). Drug resistance in an immunological model of HIV-1 infection with impulsive drug effects. Bulletin of Mathematical Biology, 67(4), 783–813. https://doi.org/10.1016/j.bulm.2004.10.004
   PubMed Web of Science ®Google Scholar
• Wang, Y., Zhang, J., & Liu, M. (2014). Exponential stability of impulsive positive systems with mixed time-varying delays. IET Control Theory & Applications, 8(15), 1537–1542. https://doi.org/10.1049/cth2.v8.15
   Web of Science ®Google Scholar
• Wu, Q., Song, Q., Hu, B., Zhao, Z., Liu, Y., & Alsaadi, F. E. (2020). Robust stability of uncertain fractional-order singular systems with neutral and time-varying delays. Neurocomputing, 401, 145–152. https://doi.org/10.1016/j.neucom.2020.03.015
   Web of Science ®Google Scholar
• Xiao, X., Park, J. H., & Zhou, L. (2019). Stabilization of switched linear singular systems with state reset. Journal of the Franklin Institute, 356(1), 237–247. https://doi.org/10.1016/j.jfranklin.2018.10.018
   Web of Science ®Google Scholar
• Xu, J., & Sun, J. (2010). Finite-time stability of linear time-varying singular impulsive systems. IET Control Theory & Applications, 4(10), 2239–2244. https://doi.org/10.1049/iet-cta.2010.0242
   Web of Science ®Google Scholar
• Xue, Y. Q., & Zhao, P. (2023). Input-to-state consensus of nonlinear positive multi-agent systems under state feedback and impulsive control. International Journal of Control, Automation and Systems, 21(7), 2099–2111. https://doi.org/10.1007/s12555-021-1069-x
   Web of Science ®Google Scholar
• Yang, H., & Zhang, Y. (2018). Stability of positive delay systems with delayed impulses. IET Control Theory & Applications, 12(2), 194–205. https://doi.org/10.1049/cth2.v12.2
   Web of Science ®Google Scholar
• Yang, H., & Zhang, Y. (2020). Exponential stability analysis for discrete-time homogeneous impulsive positive delay systems of degree one. Journal of the Franklin Institute, 357(4), 2295–2329. https://doi.org/10.1016/j.jfranklin.2019.11.070
   Web of Science ®Google Scholar
• Yao, J., Guan, Z. H., Chen, G., & Ho, D. W. (2006). Stability, robust stabilization and H∞ control of singular-impulsive systems via switching control. Systems & Control Letters, 55(11), 879–886. https://doi.org/10.1016/j.sysconle.2006.05.002
   Web of Science ®Google Scholar
• Zhang, J., Wang, Y., Xiao, J., & Guan, Z. (2014). Stability analysis of impulsive positive systems. IFAC Proceedings Volumes, 47(3), 5987–5991. https://doi.org/10.3182/20140824-6-ZA-1003.00021
   Google Scholar
• Zhang, Y. (2012). Exponential stability of impulsive discrete systems with time delays. Applied Mathematics Letters, 25(12), 2290–2297. https://doi.org/10.1016/j.aml.2012.06.019
   Web of Science ®Google Scholar
• Zhao, P., Kang, Y., Niu, B., & Wang, X. (2022). Stochastic stability and stabilization of positive Markov jump linear impulsive systems with time delay. IET Control Theory & Applications, 16(17), 1731–1738. https://doi.org/10.1049/cth2.v16.17
   Web of Science ®Google Scholar
• Zhao, P., Kang, Y., Niu, B., & Zhao, Y. (2023). Input-to-state stability and stabilization for switched nonlinear positive systems. Nonlinear Analysis: Hybrid Systems, 47, 101298.  https://doi.org/10.1016/j.nahs.2022.101298
   Web of Science ®Google Scholar
• Zhao, S., Sun, S., & Liu, L. (2008). Finite-time stability of linear time-varying singular systems with impulsive effects. International Journal of Control, 81(11), 1824–1829. https://doi.org/10.1080/00207170801898893
   Web of Science ®Google Scholar