Abstract
This paper studies the finite-time \({{H}_{\infty }}\) stability analysis of uncertain network-based control systems under random data packet dropout and varying network delay. The system considered as an uncertain discrete-time stochastic system benefits from Bernoulli distributed white sequence technique for modeling the packet dropout. Sufficient conditions by means of a state feedback controller are derived to suppress the inherent effects of data packet dropout and network delay simultaneously. Simulations are provided to illustrate the feasibility and applicability of the control algorithm proposed in this paper.
Similar content being viewed by others
References
Shi, Y., Yu, B.: Robust mixed \({H}_{2}/{{H}_{\infty }}\) control of networked control systems with random time delays in both forward and backward communication links. Automatica 47(4), 754–760 (2011)
Rasool, S.C.F., Swain, S.K.N.A.: Robust mode delay-dependent \({{H}_{\infty }}\) control of discrete-time systems with random communication delays. IET Control Theory Appl. 4(6), 936–944 (2010)
Sun, J., Jiang, J.: Delay and data packet dropout separately related stability and state feedback stabilisation of networked control systems. IET Control Theory Appl. 7(3), 333–342 (2013)
Li, H., Sun, Z., Liu, H., Sun, F.: Stabilisation of networked control systems using delay-dependent control gains. IET Control Theory Appl. 6(5), 698–706 (2012)
Wang, S., Yu, M., Sun, X.: Robust \({{H}_{\infty }}\) control for time-delay networked control systems with probability constraints. IET Control Theory Appl. 9(16), 2482–2489 (2015)
Ishido, Y., Takaba, K., Quevedo, D.E.: Stability analysis of networked control systems subject to packet-dropouts and finite-level quantization. Syst. Control Lett. 60(5), 325–332 (2011)
Argha, A., Li, L., Su, S., Nguyen, H.: Stabilising the networked control systems involving actuation and measurement consecutive packet losses. IET Control Theory Appl. 10(11), 1269–1280 (2016)
Qu, F., Guan, Z., Li, T., Yuan, F.: Stabilisation of wireless networked control systems with packet loss. IET Control Theory Appl. 6(15), 2362–2366 (2012)
Yang, R., Liu, G.P., Shi, P., Thomas, C., Basin, M.V.: Predictive output feedback control for networked control systems. IEEE Trans. Ind. Electron. 61(1), 512–520 (2014)
Shen, M., Park, J.H., Ye, D.: A separated approach to control of Markov jump nonlinear systems with general transition probabilities. IEEE Trans. Cybern. 46(9), 2010–2018 (2016)
Shen, M., Park, J.H.: \({{H}_{\infty }}\) filtering of Markov jump linear systems with general transition probabilities and output quantization. ISA Trans. 63, 204–210 (2016)
Shen, M., Ye, D.: Improved fuzzy control design for nonlinear Markovian-jump systems with incomplete transition descriptions. Fuzzy Sets Syst. 217, 80–95 (2013)
Shen, M., Ye, D., Wang, Q.G.: Mode-dependent filter design for Markov jump systems with sensor nonlinearities in finite frequency domain. Signal Process. 134, 1–8 (2017)
Shen, M., Lim, C., Shi, P.: Reliable \({{H}_{\infty }}\) static output control of linear time varying delay systems against sensor failures. Int. J. Robust Nonlinear Control 302, 65–81 (2016)
Tabbara, M., Nesic, D., Teel, A.R.: Stability of wireless and wireline networked control systems. IEEE Trans. Autom. Control 52(9), 1615–1630 (2007)
Huang, D., Nguang, S.K.: State feedback control of uncertain networked control systems with random time delays. IEEE Trans. Autom. Control 53(3), 829–834 (2008)
Zhao, H., Wu, M., Liu, G., She, J.: \({{H}_{\infty }}\) control for networked control systems (NCS) with time-varying delays. J. Control Theory Appl. 2, 157–162 (2005)
Zhang, L., Shi, Y., Chen, T., Huang, B.: A new method for stabilization of networked control systems with random delays. IEEE Trans. Autom. Control 50(8), 1177–1181 (2005)
Wang, Z., Member, S., Yang, F., Ho, D.W.C., Liu, X.: Robust \({{H}_{\infty }}\) control for networked systems with random packet losses. IEEE Trans. Syst. Man Cybern. B Cybern. 37(4), 916–924 (2007)
Guo, G.: A switching system approach to sensor and actuator assignment for stabilisation via limited multi-packet transmitting channels. Int. J. Control 84(1), 78–93 (2011)
Guo, G., Lu, Z., Han, Q.: Control with Markov sensors/actuators assignment. IEEE Trans. Autom. Control 57(7), 1799–1804 (2012)
Liu, K., Fridman, E.: Networked-based stabilization via discontinuous Lyapunov functionals. Int. J. Robust Nonlinear Control 22(4), 420–436 (2012)
Klinkhieo, S., Kambhampati, C., Patton, R.J.: Fault tolerant control in NCS medium access constraints. In: 2007 IEEE International Conference on Networking, Sensing and Control, pp. 416–423 (2007)
Song, H., Zhang, W., Yu, L.: \({{H}_{\infty }}\) filtering of network-based systems with communication constraints. IET Signal Process. 4(1), 69–77 (2010)
Tan, C., Li, L., Zhang, H.: Stabilization of networked control systems with both network-induced delay and packet dropout. Automatica 59, 194–199 (2015)
Meng, X., Lam, J., Gao, H.: Network based \({{H}_{\infty }}\) control for stochastic systems. Int. J. Robust Nonlinear Control 19(3), 295–312 (2009)
Wang, G., Li, L., Wu, B.: Robust stability of nonlinear model-based networked control systems with time-varying transmission times. Nonlinear Dyn. 69(3), 1351–1363 (2012)
Wen, S., Zeng, Z., Huang, T.: Robust \({{H}_{\infty }}\) output tracking control for fuzzy networked systems with stochastic sampling and multiplicative noise. Nonlinear Dyn. 70(2), 1061–1077 (2012)
Tahoun, A.H.: Adaptive stabilizer for chaotic networked systems with network-induced delays and packet losses. Nonlinear Dyn. 81(1–2), 823–832 (2015)
Weiss, L., Infante, E.F.: Finite time stability under perturbing forces and on product spaces. IEEE Trans. Autom. Control 12(1), 54–59 (1967)
Dorato, P.: Short-time stability in linear time-varying systems. DTIC Document (1961)
Amato, F., Ariola, M., Dorato, P.: Finite-time control of linear systems subject to parametric uncertainties and disturbances. Automatica 37(9), 1459–1463 (2001)
Zhao, J., Shen, H., Li, B., Wang, J.: Finite-time \({{H}_{\infty }}\) control for a class of Markovian jump delayed systems with input saturation. Nonlinear Dyn. 73(1), 1099–1110 (2013)
Du, H., Cheng, Y., He, Y., Jia, R.: Finite-time output feedback control for a class of second-order nonlinear systems with application to DC–DC buck converters. Nonlinear Dyn. 78(3), 2021–2030 (2014)
Cai, M., Xiang, Z., Guo, J.: Adaptive finite-time control for uncertain nonlinear systems with application to mechanical systems. Nonlinear Dyn. 84(2), 943–958 (2015)
Golestani, M., Mohammadzaman, I., Yazdanpanah, M.J.: Robust finite-time stabilization of uncertain nonlinear systems based on partial stability. Nonlinear Dyn. 85(1), 87–96 (2016)
Zuo, Z., Li, H., Wang, Y.: New criterion for finite-time stability of linear discrete-time systems with time-varying delay. J. Frankl. Inst. 350(9), 2745–2756 (2013)
Zhang, Z., Zhang, Z., Zhang, H., Zheng, B.: Finite-time stability analysis and stabilization for linear discrete-time system with time-varying delay. J. Frankl. Inst. 351(6), 3457–3476 (2014)
Liu, A., Yu, L., Zhang, D., Zhang, W.: Finite-time \({{H}_{\infty }}\) control for discrete-time genetic regulatory networks with random delays and partly unknown transition probabilities. Frankl. Inst. 350(7), 1944–1961 (2013)
Elahi, A., Alfi, A.: Finite-time \({{H}_{\infty }}\) control of uncertain networked control systems with randomly varying communication delays. ISA Trans. 69, 65–88 (2017)
Mastellone, S., Abdallah, C.T., Dorato, P.: Stability and finite-time stability analysis of discrete-time nonlinear networked control systems. In: Proceedings of the American Control Conference, 2005, vol. 2, pp. 1239–1244 (2005)
Dritsas, L., Nikolakopoulos, G., Tzes, A.: Constrained finite time control of networked systems with uncertain delays. In: 14th Mediterranean Conference on Control and Automation, pp. 1–6. MED’06 (2006)
Mastellone, S., Dorato, P., Abdallah, C.T.: Finite-time stability for nonlinear networked control systems. In: Current Trends in Nonlinear Systems and Control, pp. 535–553 (2006)
Shang, Y., Gao, F., Yuan, F.: Finite-time stabilization of networked control systems subject to communication delay. Int. J. Adv. Comput. Technol. 3(3), 192–198 (2011)
Sun, Y., Xu, J.: Finite-time boundedness and stabilization of networked control systems with time delay. Math. Probl. Eng. 2012, 1–12 (2012)
Sun, Y.: Finite-time boundedness and stabilisation of networked control systems with bounded packet dropout. Int. J. Syst. Sci. 45(9), 37–41 (2014)
Hua, C., Yu, S., Guan, X.: Finite-time control for a class of networked control systems with short time-varying delays and sampling jitter. Int. J. Autom. Comput. 12(4), 448–454 (2015)
Mathyalagan, K., Park, J., Sakthivel, R.: Finite-time boundedness and dissipativity analysis of networked cascade control systems. Nonlinear Dyn. 84(4), 2149–2160 (2016)
Sun, Y., Li, G.: Finite-time stability and stabilization of networked control systems with bounded packet dropout. Discrete Dyn. Nat. Soc. 2014, 1–6 (2014)
Amato, F., Ariola, M.: Finite-time control of discrete-time linear systems. IEEE Trans. Autom. Control 50(5), 724–729 (2005)
Zhang, Y., Liu, C., Sun, H.: Robust finite-time \({{H}_{\infty }}\) control for uncertain discrete jump systems with time delay. Appl. Math. Comput. 219(5), 2465–2477 (2012)
Boyd, S.P.: Linear Matrix Inequalities in System and Control Theory, vol. 15. SIAM, Philadelphia (1994)
Stojanovic, S.B., Debeljkovic, D.L., Dimitrijevic, N.: Finite-time stability of discrete-time systems with time-varying delay. Chem. Ind. Chem. Eng. Q. CICEQ 18(4–1), 525–533 (2012)
Gao, S., Tang, G.: Stabilization of networked control systems with random delays. IEEE Trans. Ind. Electron. 58(9), 3250–3255 (2011)
Yang, F., Wang, Z., Hung, Y., Gani, M.: \({{H}_{\infty }}\) control for networked systems with random communication delays. IEEE Trans. Autom. Control 51(3), 511–518 (2006)
Wang, C., Chu, R., Ma, J.U.N.: Controlling a chaotic resonator by means of dynamic track control. Complexity 21(1), 370–378 (2015)
Li, X., Sun, S.: \({{H}_{\infty }}\) control for networked systems with random delays and packet dropouts. Int. J. Control Autom. Syst. 10(5), 1023–1031 (2012)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Elahi, A., Alfi, A. Finite-time \({{H}_{\infty }}\) stability analysis of uncertain network-based control systems under random packet dropout and varying network delay. Nonlinear Dyn 91, 713–731 (2018). https://doi.org/10.1007/s11071-017-3905-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-017-3905-3