Current Science

Open Access Open Access  Restricted Access Subscription Access

Improved Criteria on Robust Analysis for Linear System Using Convex Combination and Geometric Sequence Methods


Affiliations
1 College of Electrical and Information Engineering, Southwest Minzu University, Chengdu 610041, China
 

This article addresses the robust analysis on a delayed system with uncertainties. A geometric sequence division(GSD) method is applied for delay partition.Then, a GSD-dependent Lyapunov–Krasovskii functional(LKF) is newly proposed, in which the integral interval relevant with the state variables forms in geometric progression. In addition, by applying the convex combination method, parameter uncertainties and the delay derivative d(t) can thus be flexibly overcome. As a result, unnecessary enlargement for estimating the LKF derivative is eliminated. Numerical example shows that this proposed work achieves expected results.

Keywords

Convex Combination, Delay Partition, Geometric Sequence, Parameter Uncertainties.
User
Notifications
Font Size

  • Richard, J. P., Time-delay systems: an overview of some recent advances and open problems. Automatica, 2003, 39, 1667–1694.

  • Ekramian, M., Ataei, M. and Talebi, S., Stability of nonlinear time-delay systems satisfying a quadratic constraint. Trans. Inst. Meas. Control, 2016; doi:10.1177/0142331216668003.

  • Fridman, E. and Shaikhet, L., Delay-induced stability of vector second-order systems via simple Lyapunov functionals. Automatica, 2016, 74, 288–296.

  • Gouaisbaut, F. and Peaucelle, D., Delay-dependent stability analysis of linear time delay systems, IFAC Workshop on Time Delay System (TDS’06), L’Aquila, Italy, 2006.

  • Wu, Z.-G., Shi, P., Su, H. and Chu, J., Local synchronization of chaotic neural networks with sampled- data and saturating actuators. IEEE Trans. Cybernetics, 2014, 44, 2635–2645.

  • Shi, K., Liu, X., Zhu, H., Zhong, S., Liu, Y. and Yin, C., Novel integral inequality approach on master-slave synchronization of chaotic delayed Lur’s systems with sampled-data feedback control. Nonlinear Dynam., 2016, 83, 1259–1274.

  • Hua, C. C., Yang, X., Yan, J. and Guan, X. P., New exponential stability criteria for neural networks with time-varying delay. IEEE Trans. Circuits Systems II: Exp. Briefs, 2011, 58, 931–935.

  • Zheng, C. D., Zhang, H. and Wang, Z., Novel exponential stability criteria of high-order neural networks with time-varying delays. IEEE Trans. Syst. Man Cyb., 2011, 41, 486–496.

  • Shi, K., Liu, X., Tang, Y., Zhu, H. and Zhong, S., Some novel approaches on state estimation of delayed neural networks. Inform. Sci., 2016, 372, 313–331.

  • Lakshmanan, S., Park, J. H., Jung, H., Kwon, O. and Rakkiyappan, R., A delay partitioning approach to delay-dependent stability analysis for neutral type neural networks with discrete and distributed delays. Neurocomputing, 2013, 111, 81–89.

  • Gyurkovics, É., A note on Wirtinger-type integral inequalities for time-delay systems. Automatica, 2015, 61, 44–46.

  • Niamsup, P., Ratchagit, K. and Phat, V., Novel criteria for finite-time stabilization and guaranteed cost control of delayed neural networks. Neurocomputing, 2015, 160, 281–286.

  • Zhang, H., Wang, J., Wang, Z. and Liang, H., Mode-dependent stochastic synchronization for Markovian coupled neural networks with time-varying mode-delays. IEEE Trans. Neural Net. Learn. Syst., 2015, 26, 2621–2634.

  • Wang, C. and Shen, Y., Delay partitioning approach to robust stability analysis for uncertain stochastic systems with interval time-varying delay. IET Control Theory Appl., 2012, 6, 875–883.

  • Sun, J., Liu, G., Chen, J. and Rees, D., Improved delay-range-dependent stability criteria for linear systems with time-varying delays. Automatica, 2010, 46, 466–470.

  • Gao, H. and Chen, T., Stabilization of nonlinear systems under variable sampling: a fuzzy control approach. IEEE Trans. Fuzzy Syst., 2007, 15, 972–983.

  • Fridman, E., Shaked, U. and Liu, K., New conditions for delay-derivative-dependent stability. Automatica, 2009, 45, 2723–2727.

  • Park, P., Ko, J. W. and Jeong, C., Reciprocally convex approach to stability of systems with time-varying delays. Automatica, 2011, 47, 235–238.

  • Seuret, A. and Gouaisbaut, F., Wirtinger-based integral inequality: application to time-delay systems. Automatica, 2013, 49, 2860–2866.

  • Chen, W.-H., Jiang,Z., Lu, X. and Luo, S., H∞ synchronization for complex dynamical networks with coupling delays using distributed impulsive control. Nonlinear Anal: Hybrid Syst., 2015, 17, 111–127.

  • Kchaou, M., Hajjaji, A. E. and Toumi, A., Non-fragile H∞ output feedback control design for continuous-time fuzzy systems. ISA Trans., 2015, 54, 3–14.

  • Tang, Z., Park, J. H. and Lee, T. H., Dynamic output-feedback-based design for networked control systems with multipath packet dropouts. Appl. Math. Comput., 2016, 275, 121–133.

  • Tang, Z., Park, J. H. and Feng, J., Impulsive effects on quasisynchronization of neural networks with parameter mismatches and time-varying delay. IEEE Trans. Neural Net. Learn. Syst., 2017; doi:10.1109/TNNLS.2017.265102412.

  • Ali, M. S. and Saravanan, S., Robust finite-time H∞ control for a class of uncertain switched neural networks of neutral-type with distributed time varying delays. Neurocomputing, 2016, 177, 454–468.

  • Shi, K., Tang, Y., Liu, X. and Zhong, S., Non-fragile sampleddata robust synchronization of uncertain delayed chaotic Lurie systems with randomly occurring controller gain fluctuation. ISA Trans., 2017, 66, 185–199.

  • Bouarar, T., Guelton, K. and Manamanni, N., Robust fuzzy Lyapunov stabilization for uncertain and disturbed Takagi-Sugeno descriptors. ISA Trans., 2010, 49, 447–461.

  • Khazaee, M., Markazi, A. H. and Omidi, E., Adaptive fuzzy predictive sliding control of uncertain nonlinear systems with bound-known input delay. ISA Trans., 2015, 59, 314–324.

  • Liu, Y. and Li, M., Improved robust stabilization method for linear systems with interval time-varying input delays by using Wirtinger inequality. ISA Trans., 2015, 56, 111–122.

  • Zeng, H., He, Y., Wu, M. and She, J., Free-matrix-based integral inequality for stability analysis of systems with time-varying delay. IEEE Trans. Automat. Control, 2015, 60, 2768–2772.

  • Wang, Z., Liu, L., Shan, Q.-H. and Zhang, H., Stability criteria for recurrent neural networks with time-varying delay based on secondary delay partitioning method. IEEE Trans. Neural Net. Learn. Syst., 2015, 26, 2589–2595.

  • Park, P., Lee, W. I. and Lee, S. Y., Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems. J. Frank. Inst., 2015, 352, 1378–1396.

  • de Oliveira, M. C. and Skelton, R. E., Stability tests for constrained linear systems. Perspectives in Robust Control (ed. Moheimani, S. R.), Springer-Verlag, Berlin, 2001, pp. 241–257.

  • Lee, W. I., Lee, S. Y. and Park, P., Improved criteria on robust stability and performance for linear systems with interval timevarying delays via new triple integral functionals. Appl. Math. Comput., 2014, 243, 570–577.

  • Peng, C. and Tian, Y.-C., Improved delay-dependent robust stability criteria for uncertain systems with interval time-varying delay. IET Control Theory Appl., 2008, 2, 752–761.

  • Zhao, Y., Gao, H., Lam, J. and Du, B., Stability and stabilization of delayed T–S fuzzy systems: a delay partitioning approach. IEEE Trans. Fuzzy Syst., 2009, 17, 750–762.


Abstract Views: 331

PDF Views: 99




  • Improved Criteria on Robust Analysis for Linear System Using Convex Combination and Geometric Sequence Methods

Abstract Views: 331  |  PDF Views: 99

Authors

Hao Chen
College of Electrical and Information Engineering, Southwest Minzu University, Chengdu 610041, China
Huazhang Wang
College of Electrical and Information Engineering, Southwest Minzu University, Chengdu 610041, China
Zhenzhen Zhang
College of Electrical and Information Engineering, Southwest Minzu University, Chengdu 610041, China

Abstract


This article addresses the robust analysis on a delayed system with uncertainties. A geometric sequence division(GSD) method is applied for delay partition.Then, a GSD-dependent Lyapunov–Krasovskii functional(LKF) is newly proposed, in which the integral interval relevant with the state variables forms in geometric progression. In addition, by applying the convex combination method, parameter uncertainties and the delay derivative d(t) can thus be flexibly overcome. As a result, unnecessary enlargement for estimating the LKF derivative is eliminated. Numerical example shows that this proposed work achieves expected results.

Keywords


Convex Combination, Delay Partition, Geometric Sequence, Parameter Uncertainties.

References





DOI: https://doi.org/10.18520/cs%2Fv113%2Fi06%2F1081-1089