Stability analysis for singular random impulsive control system: a novel neutral impulsive delay system approach. (English) Zbl 1538.34279
Summary: The paper studies stability analysis for an uncertain singular time varying delay system (USTDS) under random impulsive control (RIC). It also proves the stability results for a singular impulsive time delay system in terms of neutral impulsive time delay system approach. Besides, we derive the new sufficient conditions for stability results like exponential stability (ES) and robust exponential stability (RES) of the proposed system via linear matrix inequality (LMI) by employing the Lyapunov-Krasovskii functional (LKF) approach. In addition, two numerical examples, along with graphical simulations, are provided to illustrate the validity and effectiveness of the proposed results.
{© 2023 John Wiley & Sons, Ltd.}
{© 2023 John Wiley & Sons, Ltd.}
MSC:
| 34K20 | Stability theory of functional-differential equations |
| 93D09 | Robust stability |
| 37C60 | Nonautonomous smooth dynamical systems |
| 34K45 | Functional-differential equations with impulses |
| 34K40 | Neutral functional-differential equations |
| 34K50 | Stochastic functional-differential equations |
| 34K35 | Control problems for functional-differential equations |
Keywords:
Lyapunov-Krasovskii functional; random impulsive control; singular time varying delay systems; stability analysisReferences:
| [1] | G.Liu, New results on stability analysis of singular time‐delay systems, International Journal of Systems Science48 (2017), no. 7, 1395-1403. · Zbl 1362.93109 |
| [2] | C.Noreddine, B. A.Sadek, T.El Houssaine, and B.Boukili, Improved results on stability criteria for singular systems with interval time‐varying delays, Journal of Circuits, Systems and Computers30 (2021), no. 01, 2130001. |
| [3] | Z.‐Y.Liu, C.Lin, and B.Chen, A neutral system approach to stability of singular time‐delay systems, Journal of the Franklin Institute351 (2014), no. 10, 4939-4948. · Zbl 1395.93466 |
| [4] | T. H.Luu and P. T.Nam, Stability analysis of singular time‐delay systems using the auxiliary function‐based double integral inequalities, International Journal of Systems Science52 (2021), no. 9, 1868-1881. · Zbl 1483.93469 |
| [5] | Z.Shu and J.Lam, Exponential estimates and stabilization of uncertain singular systems with discrete and distributed delays, International Journal of Control81 (2008), no. 6, 865-882. · Zbl 1152.93462 |
| [6] | W.Xue and W.Mao, Admissible finite‐time stability and stabilization of uncertain discrete singular systems, Journal of Dynamic Systems, Measurement, and Control135 (2013), no. 3, 031018. |
| [7] | J.Lin and L.Rong, Robust stability and stabilization for singular time‐delay systems with linear fractional uncertainties: a strict LMI approach, Mathematical Problems in Engineering2013 (2013). · Zbl 1299.93225 |
| [8] | P. L.Liu, Improved delay‐dependent robust exponential stabilization criteria for uncertain time‐varying delay singular systems, International Journal of Innovative Computing, Information and Control9 (2013), no. 1, 165-178. |
| [9] | X.Yang, X.Li, and J.Cao, Robust finite‐time stability of singular nonlinear systems with interval time‐varying delay, Journal of the Franklin Institute355 (2018), no. 3, 1241-1258. · Zbl 1393.93101 |
| [10] | Y.Han, Y.Kao, C.Gao, and B.Jiang, Robust sliding mode control for uncertain discrete singular systems with time‐varying delays, International Journal of Systems Science48 (2017), no. 4, 818-827. · Zbl 1358.93047 |
| [11] | G.Zhuang, J.Xia, B.Zhang, and W.Sun, Robust normalisation and p-d state feedback control for uncertain singular Markovian jump systems with time‐varying delays, IET Control Theory & Applications12 (2017), no. 3, 419-427. |
| [12] | J.Wang, Q.Zhang, D.Xiao, and F.Bai, Robust stability analysis and stabilisation of uncertain neutral singular systems, International Journal of Systems Science47 (2016), no. 16, 3762-3771. · Zbl 1346.93313 |
| [13] | G.Liu, S.Xu, Y.Wei, Z.Qi, and Z.Zhang, New insight into reachable set estimation for uncertain singular time‐delay systems, Applied Mathematics and Computation320 (2018), 769-780. · Zbl 1426.93023 |
| [14] | C.Yin, S.Zhong, X.Huang, and Y.Cheng, Robust stability analysis of fractional‐order uncertain singular nonlinear system with external disturbance, Applied Mathematics and Computation269 (2015), 351-362. · Zbl 1410.93100 |
| [15] | S.Zhao, J.Sun, and L.Liu, Finite‐time stability of linear time‐varying singular systems with impulsive effects, International Journal of Control81 (2008), no. 11, 1824-1829. · Zbl 1148.93345 |
| [16] | J.Xu and J.Sun, Finite‐time stability of linear time‐varying singular impulsive systems [brief paper], IET Control Theory & Applications4 (2010), no. 10, 2239-2244. |
| [17] | I.Zamani, M.Shafiee, and A.Ibeas, On singular hybrid switched and impulsive systems, International Journal of Robust and Nonlinear Control28 (2018), no. 2, 437-465. · Zbl 1390.93676 |
| [18] | S.Shi, Q.Zhang, Z.Yuan, and W.Liu, Hybrid impulsive control for switched singular systems, IET Control Theory & Applications5 (2011), no. 1, 103-111. |
| [19] | W.Tao, Y.Liu, and J.Lu, Stability and l2‐gain analysis for switched singular linear systems with jumps, Mathematical Methods in the Applied Sciences40 (2017), no. 3, 589-599. · Zbl 1365.34026 |
| [20] | Z.‐H.Guan, C. W.Chan, A. Y. T.Leung, and G.Chen, Robust stabilization of singular‐impulsive‐delayed systems with nonlinear perturbations, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications48 (2001), no. 8, 1011-1019. · Zbl 1003.93044 |
| [21] | W.‐H.Chen and W. X.Zheng, Robust stability and h‐control of uncertain impulsive systems with time‐delay, Automatica45 (2009), no. 1, 109-117. · Zbl 1154.93406 |
| [22] | W.‐H.Chen, R.Jiang, X.Lu, and W. X.Zheng, H control of linear singular time‐delay systems subject to impulsive perturbations, IET Control Theory & Applications11 (2016), no. 3, 420-428. |
| [23] | W.‐H.Chen, W. X.Zheng, and X.Lu, Impulsive stabilization of a class of singular systems with time‐delays, Automatica83 (2017), 28-36. · Zbl 1373.93268 |
| [24] | T.Zhan, S.Ma, X.Liu, and H.Chen, Exponential stability and h control of uncertain singular nonlinear switched systems with impulsive perturbations, International Journal of Systems Science50 (2019), no. 13, 2424-2436. · Zbl 1483.93531 |
| [25] | J.Yao, Z.‐H.Guan, G.Chen, and D. W. C.Ho, Stability, robust stabilization and h control of singular‐impulsive systems via switching control, Systems & Control Letters55 (2006), no. 11, 879-886. · Zbl 1113.93096 |
| [26] | T.Zhan, S.Ma, and H.Chen, Impulsive stabilization of nonlinear singular switched systems with all unstable‐mode subsystems, Applied Mathematics and Computation344 (2019), 57-67. · Zbl 1428.93095 |
| [27] | C.Zhou and H.Jiang, Robust fuzzy control of nonlinear fuzzy impulsive singular perturbed systems with time‐varying delay, Int. J. Math. Comput. Phys. Elect. Comput. Eng.6 (2012), no. 8, 851-856. |
| [28] | R.Agarwal, S.Hristova, and D.O’Regan, Exponential stability for differential equations with random impulses at random times,Advances in Difference Equations2013 (2013), no. 1, 372. · Zbl 1347.34024 |
| [29] | X.Li, A.Vinodkumar, and T.Senthilkumar, Exponential stability results on random and fixed time impulsive differential systems with infinite delay, Mathematics7 (2019), no. 9, 843. |
| [30] | A.Vinodkumar, T.Senthilkumar, Z.Liu, and X.Li, Exponential stability of random impulsive pantograph equations, Mathematical Methods in the Applied Sciences44 (2021), no. 8, 6700-6715. · Zbl 1508.34111 |
| [31] | W.Hu and Q.Zhu, Moment exponential stability of stochastic nonlinear delay systems with impulse effects at random times, International Journal of Robust and Nonlinear Control29 (2019), no. 12, 3809-3820. · Zbl 1426.93353 |
| [32] | W.Hu and Q.Zhu, Exponential stability of stochastic differential equations with impulse effects at random times, Asian Journal of Control (2020). · Zbl 07872623 |
| [33] | W.Hu and Q.Zhu, Moment exponential stability of stochastic delay systems with delayed impulse effects at random times and applications in the stabilisation of stochastic neural networks, International Journal of Control (2019), 1-11. |
| [34] | A.Vinodkumar, T.Senthilkumar, and X.Li, Robust exponential stability results for uncertain infinite delay differential systems with random impulsive moments, Advances in Difference Equations2018 (2018), no. 1, 39. · Zbl 1445.34106 |
| [35] | T.Senthilkumar, A.Vinodkumar, and M.Gowrisankar, Stability results on random impulsive control for uncertain neutral delay differential systems, International Journal of Control (2022), 1-13. |
| [36] | A.Vinodkumar, T.Senthilkumar, S.Hariharan, and J.Alzabut, Exponential stabilization of fixed and random time impulsive delay differential system with applications, Mathematical Biosciences and Engineering18 (2021), no. 3, 2384-2400. · Zbl 1471.93229 |
| [37] | A.Vinodkumar, T.Senthilkumar, H.Işık, S.Hariharan, and N.Gunasekaran, An exponential stabilization of random impulsive control systems and its application to chaotic systems, Mathematical Methods in the Applied Sciences (2022). |
| [38] | Z.Du, S.Hu, and J.Li, Event‐triggered h‐infinity stabilization for singular systems with state delay, Asian Journal of Control23 (2021), no. 2, 835-846. · Zbl 07878853 |
| [39] | K.Gu, J.Chen, and V. L.Kharitonov, Stability of time‐delay systems, Springer Science & Business Media, 2003. · Zbl 1039.34067 |
| [40] | S.Boyd, L.El Ghaoui, E.Feron, and V.Balakrishnan, Linear matrix inequalities in system and control theory, SIAM, 1994. · Zbl 0816.93004 |
| [41] | E.‐K.Boukas, Control of singular systems with random abrupt changes, Springer Science & Business Media, 2008. · Zbl 1144.93029 |
| [42] | X.Tang and Z.Liu, Sliding mode observer‐based adaptive control of uncertain singular systems with unknown time‐varying delay and nonlinear input, ISA transactions (2021). |
| [43] | C.Maharajan, R.Raja, J.Cao, G.Rajchakit, Z.Tu, and A.Alsaedi, Lmi‐based results on exponential stability of bam‐type neural networks with leakage and both time‐varying delays: A non‐fragile state estimation approach, Applied Mathematics and Computation326 (2018), 33-55. · Zbl 1426.93238 |
| [44] | S.Pandiselvi, R.Raja, J.Cao, X.Li, and G.Rajchakit, Impulsive discrete‐time grns with probabilistic time delays, distributed and leakage delays: an asymptotic stability issue, IMA Journal of Mathematical Control and Information36 (2019), no. 1, 79-100. · Zbl 1417.92057 |
| [45] | R.Sakthivel, R.Raja, and S. M.Anthoni, Linear matrix inequality approach to stochastic stability of uncertain delayed bam neural networks, IMA Journal of Applied Mathematics78 (2013), no. 6, 1156-1178. · Zbl 1281.93104 |
| [46] | A.Pratap, R.Raja, C.Sowmiya, O.Bagdasar, J.Cao, and G.Rajchakit, Robust generalized mittag‐leffler synchronization of fractional order neural networks with discontinuous activation and impulses, Neural Networks103 (2018), 128-141. · Zbl 1441.93239 |
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