Criteria for finite-time stability of singular large-scale discrete-time delay systems
DOI:
https://doi.org/10.56764/hpu2.jos.2023.2.2.11-21Abstract
This paper concerns a problem of finite-time stability for a class of linear singular large-scale systems with delays. Based on matrix transformations, Lyapunov function method combined with new estimation techniques, we derive sufficient conditions for solving the finite-time stability of the system. A numerical example is given to illustrate the validity and effectiveness of the theoretical results.
References
. F. Amato, R. Ambrosino, M. Ariola, C. Cosentino, G. De Tommasi, Finite-Time Stability and Control, Lecture Notes in Control and Information Sciences, Springer-Verlag London, 453 (2014).
. L. Dai, Singular Control System, Lecture Notes in Control and Information Sciences, Berlin Springer-Verlag, (1989).
. P. Dorato, “Short time stability in linear time-varying systems”, Proc IRE Int Convention Record, Part 4, (1961) 83-87.
. N. H. Du, V. H. Linh, V. Mehrmann, D. D. Thuan, “Stability and robust stability of linear time-invariant delay differential-algebraic equations”, SIAM Journal on Matrix Analysis and Applications, 34 (2013) 1631 - 1654.
. J. K. Hale, Theory of Functional Differential Equations, Springer – Verlag, New York, (1977).
. L. V. Hien, “An explicit criterion for finite – time stability of linear nonautonomous system with delays”, Applied Mathematics Letters, 30 (2014) 12 – 18.
. Pham T. Huong, Vu N. Phat, “New results on robust finite-time stability of singular large-scale complex systems with interconnected delays”, Journal of the Franklin Institute, 358 (2021) 8678-8693.
. Pham T. Huong, Vu N. Phat, “Suboptimal finite-time control of singular large scale discrete-time”, European Journal of Control, 67 (2022) 100701.
. Kamenkov, “On stability of motion over a finite interval of time”, J. Appl. Math. Mech. 17 (1953) 529-540 (in Russian).
. V. L. Kharitonov, Time-Delay Systems: Lyapunov Functional and Matrices, Birkhauser, (2013).
. V. L. Kharitonov, “Lyapunov-Krasovskii functionals for scalar time delay equations”, Systems & Control Letters, 51 (2002) 133-149.
. O. M. Kwon, J. H. Park, “Decentralized guaranteed cost control for uncertain large-scale systems using delayed feedback: LMI optimization approach”, Journal of Optimization Theory and Applications, 129 (2006) 391-414.
. T. La –inchua, P. Niamsup, Xinzhi Liu, “Finite-Time Stability of Large-Scale Systems with Interval Time-Varying Delay in Interconnection”, Complexity (2017) 1-11.
. J. H. Park, “ Dynamic System Measure Control”, 113 (2002) 105-119.
. V. N. Phat, N. H. Muoi, and M. V. Bulatov. “Robust finite-time stability of linear differential-algebraic delay equations”, Linear Algebra and its Applications 487 (2015) 146-157.
. D. D. Siljak, Large-Scale Dynamic Systems: Stability and Structure, Dover Publications (2007).
. Nguyen T. Thanh, Vu N. Phat, “Decentralized H_ {infty} control for large-scale interconnected nonlinear time-delay systems via LMI approach”, Journal of Process Control 22 (2012) 1325-1339.
. Z. G. Wu, H. Su and P. Shi, Analysis and Synthesis of Singular Systems with Time Delays, Berlin, Springer, (2013).
Downloads
Published
How to Cite
Volume and Issue
Section
Copyright and License
Copyright (c) 2023 Thi-Huong Pham, Huu-Du Hoang, Hong-Ngoc Nguyen
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.