Magdisadek MAHMOUD, Bilal KARAKİ

10114

Discrete Networked Dynamic Systems with Eigen-Spectrum Gap: Analysis and Performance

Discrete Networked Dynamic Systems with Eigen-Spectrum Gap: Analysis and Performance

This paper provides a detailed analysis and performance treatment of a class of discrete-time systems with an eigen-spectrum gap coupled over networks. We deploy tools from time-scale modeling (TSM) theory to develop rigorous reduced-order models to aid in the stability analysis of these multiple time-scale networked systems over fixed and undirected graph topology. We establish that the controller gain matrices can be determined by solving convex optimization problems in terms of finite linear matrix inequalities with prescribed $\mathbb{H}_\infty$ and $\mathbb{H}_2$ performance criteria. As demonstrated by simulation studies, the ensuing results provide designers with a network-centric approach to improve the performance and stability of such coupled systems.
Keywords:

Discrete Network dynamic systems (DNDS) Mode separation, State dependent networks,

PDF

___

  • [1] M. S. Mahmoud, M. G. Singh, Large Scale Systems Modelling, Pergamon Press, London, 1981.
  • [2] P. Kokotovic, H. Khalil, J. O’reilly, Singular perturbation methods in control: analysis and design, Society for Industrial and Applied Mathematics, 1999.
  • [3] M. S. Mahmoud, M. G. Singh, Discrete Systems: Analysis, Control, and Optimization, Springer-Verlag, Berlin, Germany, 1984.
  • [4] H. Khalil, F. Chen, H¥-control of two-time-scale systems, Systems Control Lett., 19, (1992), 35-42.
  • [5] J. Vian, M. Sawan, H¥-control for a singularly perturbed aircraft model, Optimal Control Appl. Methods, 15, (1994), 277-289.
  • [6] E. Fridman, Robust sampled-data H¥ control of linear singularly perturbed systems, IEEE Trans. Automat. Control, 51(3), (2006), 470-475.
  • [7] M S. Mahmoud, Order reduction and control of discrete systems, Proc. IEE Part D, 129(4), (1982), 129-135.
  • [8] M S. Mahmoud, Multi-time scale analysis in discrete systems, J. Eng. Appl. Sci., 2(4), (1983), 301-315.
  • [9] M. S. Mahmoud, Y. Chen, M. G. Singh, On the eigenvalue assignment in discrete systems with slow and fast modes, Internat. J. Systems Sci., 16(1), (1985), 168-187.
  • [10] M. S. Mahmoud, Design of observer-based controllers for a class of discrete systems, Automatica, 18(3), (1982), 323-328.
  • [11] M. S. Mahmoud, Y. Chen, Design of feedback controllers by two-stage methods, Appl. Math. Model., 7(3), (1983), 163-168.
  • [12] H. A. Othman, N. M. Khraishi, Magdi S. Mahmoud, Discrete regulators with time-scale separation, IEEE Trans. Automat. Control, 30(6), (1985), 293-297.
  • [13] M. S. Mahmoud, M. G. Singh, On the use of reduced-order Models in output feedback design of discrete systems, Automatica, 21(4), (1985), 485-489.
  • [14] Y. Cao, W. Yu, W. Ren, G. Chen, An overview of recent progress in the study of distributed multi-agent coordination, IEEE Trans. Ind. Inf., 9(1), (2013), 427-438.
  • [15] H. Su, G. Jia, M.Z.Q. Chen, Semi-global containment control of multi-agent systems with intermittent input saturation, J. Frankl. Inst., 8(18), (2015), 3504-3525.
  • [16] X. Wang, H. Su, Self-triggered leader-following consensus of multi-agent systems with input time delay, Neurocomputing, 330, (2019), 70-77.
  • [17] H. Su, H. Wu, X. Chen, Observer-based discrete-time nonnegative edge synchronization of networked systems, IEEE Trans. Neural Netw. Learn. Syst., 28(10), (2017), 2446-2455.
  • [18] J. Zhang, H. Su, Time-varying formation for linear multi-agent systems based on sampled data with multiple leaders, Neurocomputing, 339, (2019), 59-65.
  • [19] H. Su, H. Wu, J. Lam, Positive edge-consensus for nodal networks via output feedback, IEEE Trans. Automat. Control, 64(3), (2019), 1244-1249.
  • [20] W. Ren, R. Bresad, E. Atkins, Information consensus in multivehicle cooperative control: collective group behavior through local interaction, IEEE Control Syst. Mag., 27(2), (2007), 71-82.
  • [21] H. Su, Y. Sun, Z. Zeng, Semi-global observer-based nonnegative edge consensus of networked systems with actuator saturation, IEEE Trans. Cybern, 50(6) (2020), 2827-2836.
  • [22] P. Liu, Z. Zeng, J. Wang, Multiple Mittag-Leffler stability of fractional-order recurrent neural networks, IEEE Trans. Syst. Man Cybern. Syst., 47(8), (2017), 2279-2288.
  • [23] H. Su, H. Wu, X. Chen, M.Z.Q. Chen, Positive edge consensus of complex networks,IEEE Trans. Syst. Man Cybern. Syst., 48(12), (2018), 2242-2250.
  • [24] P. Liu, Z. Zeng, J.Wang, Multistability analysis of a general class of recurrent neural networks with non-monotonic activation functions and time-varying delays, Neural Netw., 79, (2016), 117-127.
  • [25] X. Wang, H. Su, Consensus of hybrid multi-agent systems by event-triggered/self-triggered strategy, Appl. Math. Comput., 359, (2019), 490-501.
  • [26] H. Su, Y. Ye, X. Chen, H. He, Necessary and sufficient conditions for consensus in fractional-order multiagent systems via sampled data over directed graph, IEEE Trans. Syst. Man Cybern. Syst., (2019) Doi: 10.1109/TSMC.2019.2915653, Early Access.
  • [27] B. J. Karaki, M. S. Mahmoud, Consensus of time-delay stochastic multiagent systems with impulsive behavior and exogenous disturbances, Neurocomputing, 439, (2021), 86-95.
  • [28] B. J. Karaki, M.S. Mahmoud, Quantised scaled consensus of linear multiagent systems on faulty networks,Internat. J. Systems Sci., (2021), 1-15.
  • [29] M. S. Mahmoud, B. J. Karaki, Output-Synchronization of Discrete-Time Multiagent Systems: A Cooperative Event-Triggered Dissipative Approach, IEEE Trans. Network Sci. Eng., (2020), Doi: 10.1109/TNSE.2020.3029078, Early Access,
  • [30] H. Wu, H. Su, Discrete-time positive edge-consensus for undirected and directed nodal networks, IEEE Trans. Circuits Syst.-II:Exp. Briefs, 65(2), (2018), 221-225.
  • [31] M. S. Mahmoud, Discrete-time networked control systems, Proc. the Fourth Int. Conference on Mathematical Methods & Computational Techniques in Science & Engineering (MMCTSE 2020), London, UK, Paper 103, 2020.
  • [32] C. Godsil, G. Royle, Algebraic Graph Theory, Springer, 2001.
  • [33] M. Mesbahi, M. Egerstedt, Graph Theoretic Methods in Multiagent Networks, Princeton Univ. Press, USA, 2010.
  • [34] M. S. Mahmoud, Stabilization of discrete systems with multiple time scales, IEEE Trans. Automat. Control, 31(2), (1986), 159-162.
  • [35] D. S. Naidu, A. J. Calise, Singular perturbations and time scales in guidance and control of aerospace systems-A survey, J. Guid. Control Dyn., 24, (2001), 1057-1078.
  • [36] J. B. Rejeb, I.C. Morarescu, J. Daafouz, Synchronization in networks of linear singularly perturbed systems, Proc. Amer. Control Conf., (2016), 4293-4298.
  • [37] D. S. Naidu, Singular Perturbation Methodology in Control Systems, Peter Peregrinus Limited, Stevenage Herts, UK, 1988.
  • [38] T. H. S. Li, J. S. Chiou, F. C. Kung, Stability bounds of singularly perturbed discrete systems, IEEE Trans. Automat. Control, 44(10), (1999), 1934-1938.
  • [39] W. S. Kafri, A. E. Abed, Stability analysis of discrete-time singularly perturbed systems, IEEE Trans. Circuits Systems I Fund. Theory Appl., 43(10), (1996), 848-850.
  • [40] M. S. Mahmoud, Stabilization of discrete systems with multiple time scales, IEEE Trans. Automat. Control, 31(2), (1986), 159-162.
  • [41] D. S. Naidu, A. J. Calise, Singular perturbations and time scales in guidance and control of aerospace systems-A survey, J. Guid. Control Dyn., 24, (2001), 1057-1078.
  • [42] H. Kando, T. Iwazumi, Multirate digital control design of an optimal regulator via singular perturbation theory, Internat. J. Control, 44, (1986), 1555-1578.
  • [43] J. B. Rejeb, I.C. Morarescu, J. Daafouz, Synchronization in networks of linear singularly perturbed systems, Proc. Amer. Control Conf., (2016), 4293-4298.
  • [44] K. Zhou, J. C. Doyle, Essentials of Robust Control, Prentice-Hall, New Jersey, 1998.
  • [45] M. C. De Oliveira, J. C. Geromel, J. Bernussou, ExtendedH2 andH¥-norm characterizations and controller parametrizations for discrete-time systems, Internat. J. Control, 75(9), (2002), 666-679.
  • [46] N. Munro, S. M. Hirbad, Multivariable control of an engine/dynamometer test rig, Proc. Seventh IFAC Congress, Helsinki, (1978), 369-376.
Fundamental Journal of Mathematics and Applications-Cover
  • ISSN: 2645-8845
  • Yayın Aralığı: Yılda 4 Sayı
  • Başlangıç: 2018
  • Yayıncı: Fuat USTA
Arşiv
Sayıdaki Diğer Makaleler

Unrestricted Fibonacci and Lucas quaternions

Ahmet DAŞDEMİR, Göksal BİLGİCİ

Recurrence Relations for Knot Polynomials of Twist Knots

Kemal TAŞKÖPRÜ, Zekiye Şevval SİNAN

Construction of Degenerate $q$-Daehee Polynomials with Weight $\alpha $ and its Applications

Serkan ARACİ

Discrete Networked Dynamic Systems with Eigen-Spectrum Gap: Analysis and Performance

Magdisadek MAHMOUD, Bilal KARAKİ

$\mathfrak{I}$-Limit and $\mathfrak{I}$-Cluster Points for Functions Defined on Amenable Semigroups

Uğur ULUSU, Fatih NURAY, Erdinç DÜNDAR

Fibonacci Elliptic Biquaternions

Kahraman Esen ÖZEN, Murat TOSUN