Robust BIBO Stabilization Analysis for Discrete-time Uncertain System
The discrete-time uncertain system with time delay is investigated for bounded input bounded output (BIBO). By constructing an augmented Lyapunov function, three different sufficient conditions are established for BIBO stabilization. These conditions are expressed in the form of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. Two numerical examples are provided to demonstrate the effectiveness of the derived results.
[1] J. Luo, Fixed points and stability of neutral stochastic delay differential
equations, Journal of Mathmatical Analysis and Applications, 334 (2007)
431-440.
[2] J. Wang, L. Huang, and Z. Guo, Dynamical behavior of delayed Hopfield
neural networks with discontinuous activations, Appled Mathematical
Modelling, 33 (2009) 1793-1802.
[3] Y. Xia, Z. Huang, and M. Han, Exponential p-stability of delayed Cohen-
Grossberg-type BAM neural networks with impulses, Chaos, Solitons and
Fractals, 38 (2008) 806-818.
[4] M. Ali, P. Balasubramaniam, Stability analysis of uncertain fuzzy Hopfield
neural networks with time delays, Communications on Nonlinear Science
and Numerical Simulatation, 14 (2009) 2776-2783.
[5] J. Jiao et al., A stage-structured Holling mass defence predatorCprey
model with impulsive perturbations on predators, Journal of Computational
and Applied Mathematics, 189 (2007) 1448-1458.
[6] T. Liu, Exponential synchronization of complex delayed dynamical networks
with general topology, Physica A 387 (2008) 643-652.
[7] P. Li, Z. Yi, Synchronization analysis of delayed complex
networks with time-varying couplings, Physica A (2008),
doi:10.1016/j.physa.2008.02.008.
[8] Y. Liu, Z. Wang, and X. Liu, Robust stability of discrete-time stochastic
neural networks with time-varying delays, Neurocomputing, 71 (2008)
823-833.
[9] V. Singh, A new criterion for global robust stability of interval delayed
neural networks, Journal of Computational and Applied Mathematics, 221
(2008) 219-225.
[10] W. Xiong, L. Song, and J. Cao, Adaptive robust convergence of neural
networks with time-varying delays, Nonlinear Analysis: Real world
Application, 9 (2008) 1283-1291.
[11] D. Du, J, Bin, Robust H∞ output feedback controller design for
uncertain discrete-time switched systems via switched Lyapunov functions,
Journal of Systems Engineering and Electronics, 18 (2007) 584-590.
[12] H. Cho, J. Park, Novel delay-dependent robust stability criterion of
delayed cellular neural networks, Chaos, Solitons and Fractals, 32 (2007)
1194-1200.
[13] Q. Song, J. Cao, Global robust stability of interval neural networks with
multiple time-varying delays, Mathematical and Computer Simulation, 74
(2007) 38-46.
[14] T. Li, L. Guo, and C. Sun, Robust stability for neural networks with timevarying
delays and linear fractional uncertainties, Neurocomputing, 71
(2007) 421-427.
[15] P. Li, S. Zhong, BIBO stabilization of time-delayed system with nonlinear
perturbation, Applied Mathematics and Computation, 195 (2008)
264-269.
[16] P. Li, S. Zhong, BIBO stabilization for system with multiple mixed delays
and nonlinear perturbations, Applied Mathematics and Computation, 196
(2008) 207-213.
[17] P. Li et al., Delay-dependent robust BIBO stabilization ..., Chaos,
Solitons and Fractals (2007), doi:10.1016/j.chaos.2007.08.059.
[18] P. Li, S. Zhong, BIBO stabilization of piecewise switched linear systems
with delays and nonlinear perturbations, Appl. Math. Comput. (2009),
doi: 10.1016/j.amc.2009.03.029.
[19] Y. Fu, X. Liao, BIBO Stabilization of Stochastic Delay Systems With
Uncertainty, IEEE Transactions on Automatic Control, 48 (2003) 133-
138.
[20] Y. Huang, W. Zeng, and S. Zhong, BIBO stability of continuous time
systems, Journal of Electronic Science and Technology of China, 3 (2005)
178-181.
[21] G. Michaletzky, L. Gerencser, BIBO stability of linear switching systems,
IEEE Transactions on Automatic Control, 47 (2002) 1895-1898.
[22] Z. Guan et al., Variation of the parameters formula and the problem
of BIBO for singular measure differential systems with impulse effect,
Applied Mathematics and Computation, 60 (1994) 153-169.
[23] D. Xu, S. Zhong, The BIBO stabilization of multivariable feedback
systems, Journal of Electronic Science and Technology of China, 24
(1995) 90-96.
[24] R. Partington, C. Bonnet, H∞ and BIBO stabilization of delay systems
of neutral type, Systerm Control Letter, 52 (2004) 283-288.
[25] F. Wolfgang, Mecklenbr¨auker, On the localization of impulse responses
of BIBO-stable LSI-systems, Signal Processing, 70 (1998) 73-74.
[26] S. Kotsios, O. Feely, A BIBO stability theorem for a two-dimensional
feedback discrete system with discontinuities, Journal of Frankhn Institute,
3358 (1998) 533-537.
[27] T. Bose, M. Chen, BIBO stability of discrete bilinear system, Digital
Signal Processing, 5 (1995) 160-165.
[28] T. Lee, U. Radovic, General decentralized stabilization of large-scale
linear continuous and discrete time-delay systems, International Journal
of Control, 46 (1987) 2127-2140.
[29] B. Boyd, et al., Linear matrix inequalities in systems and control theory,
Philadelphia (PA): SIAM, 1994.
[1] J. Luo, Fixed points and stability of neutral stochastic delay differential
equations, Journal of Mathmatical Analysis and Applications, 334 (2007)
431-440.
[2] J. Wang, L. Huang, and Z. Guo, Dynamical behavior of delayed Hopfield
neural networks with discontinuous activations, Appled Mathematical
Modelling, 33 (2009) 1793-1802.
[3] Y. Xia, Z. Huang, and M. Han, Exponential p-stability of delayed Cohen-
Grossberg-type BAM neural networks with impulses, Chaos, Solitons and
Fractals, 38 (2008) 806-818.
[4] M. Ali, P. Balasubramaniam, Stability analysis of uncertain fuzzy Hopfield
neural networks with time delays, Communications on Nonlinear Science
and Numerical Simulatation, 14 (2009) 2776-2783.
[5] J. Jiao et al., A stage-structured Holling mass defence predatorCprey
model with impulsive perturbations on predators, Journal of Computational
and Applied Mathematics, 189 (2007) 1448-1458.
[6] T. Liu, Exponential synchronization of complex delayed dynamical networks
with general topology, Physica A 387 (2008) 643-652.
[7] P. Li, Z. Yi, Synchronization analysis of delayed complex
networks with time-varying couplings, Physica A (2008),
doi:10.1016/j.physa.2008.02.008.
[8] Y. Liu, Z. Wang, and X. Liu, Robust stability of discrete-time stochastic
neural networks with time-varying delays, Neurocomputing, 71 (2008)
823-833.
[9] V. Singh, A new criterion for global robust stability of interval delayed
neural networks, Journal of Computational and Applied Mathematics, 221
(2008) 219-225.
[10] W. Xiong, L. Song, and J. Cao, Adaptive robust convergence of neural
networks with time-varying delays, Nonlinear Analysis: Real world
Application, 9 (2008) 1283-1291.
[11] D. Du, J, Bin, Robust H∞ output feedback controller design for
uncertain discrete-time switched systems via switched Lyapunov functions,
Journal of Systems Engineering and Electronics, 18 (2007) 584-590.
[12] H. Cho, J. Park, Novel delay-dependent robust stability criterion of
delayed cellular neural networks, Chaos, Solitons and Fractals, 32 (2007)
1194-1200.
[13] Q. Song, J. Cao, Global robust stability of interval neural networks with
multiple time-varying delays, Mathematical and Computer Simulation, 74
(2007) 38-46.
[14] T. Li, L. Guo, and C. Sun, Robust stability for neural networks with timevarying
delays and linear fractional uncertainties, Neurocomputing, 71
(2007) 421-427.
[15] P. Li, S. Zhong, BIBO stabilization of time-delayed system with nonlinear
perturbation, Applied Mathematics and Computation, 195 (2008)
264-269.
[16] P. Li, S. Zhong, BIBO stabilization for system with multiple mixed delays
and nonlinear perturbations, Applied Mathematics and Computation, 196
(2008) 207-213.
[17] P. Li et al., Delay-dependent robust BIBO stabilization ..., Chaos,
Solitons and Fractals (2007), doi:10.1016/j.chaos.2007.08.059.
[18] P. Li, S. Zhong, BIBO stabilization of piecewise switched linear systems
with delays and nonlinear perturbations, Appl. Math. Comput. (2009),
doi: 10.1016/j.amc.2009.03.029.
[19] Y. Fu, X. Liao, BIBO Stabilization of Stochastic Delay Systems With
Uncertainty, IEEE Transactions on Automatic Control, 48 (2003) 133-
138.
[20] Y. Huang, W. Zeng, and S. Zhong, BIBO stability of continuous time
systems, Journal of Electronic Science and Technology of China, 3 (2005)
178-181.
[21] G. Michaletzky, L. Gerencser, BIBO stability of linear switching systems,
IEEE Transactions on Automatic Control, 47 (2002) 1895-1898.
[22] Z. Guan et al., Variation of the parameters formula and the problem
of BIBO for singular measure differential systems with impulse effect,
Applied Mathematics and Computation, 60 (1994) 153-169.
[23] D. Xu, S. Zhong, The BIBO stabilization of multivariable feedback
systems, Journal of Electronic Science and Technology of China, 24
(1995) 90-96.
[24] R. Partington, C. Bonnet, H∞ and BIBO stabilization of delay systems
of neutral type, Systerm Control Letter, 52 (2004) 283-288.
[25] F. Wolfgang, Mecklenbr¨auker, On the localization of impulse responses
of BIBO-stable LSI-systems, Signal Processing, 70 (1998) 73-74.
[26] S. Kotsios, O. Feely, A BIBO stability theorem for a two-dimensional
feedback discrete system with discontinuities, Journal of Frankhn Institute,
3358 (1998) 533-537.
[27] T. Bose, M. Chen, BIBO stability of discrete bilinear system, Digital
Signal Processing, 5 (1995) 160-165.
[28] T. Lee, U. Radovic, General decentralized stabilization of large-scale
linear continuous and discrete time-delay systems, International Journal
of Control, 46 (1987) 2127-2140.
[29] B. Boyd, et al., Linear matrix inequalities in systems and control theory,
Philadelphia (PA): SIAM, 1994.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:54292", author = "Zixin Liu and Shu Lü and Shouming Zhong and Mao Ye", title = "Robust BIBO Stabilization Analysis for Discrete-time Uncertain System", abstract = "The discrete-time uncertain system with time delay is investigated for bounded input bounded output (BIBO). By constructing an augmented Lyapunov function, three different sufficient conditions are established for BIBO stabilization. These conditions are expressed in the form of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. Two numerical examples are provided to demonstrate the effectiveness of the derived results.
", keywords = "Robust BIBO stabilization, delay-dependent stabilization, discrete-time system, time delay.", volume = "4", number = "8", pages = "1103-5", }
