El-Kebir Boukas

Publications (13)4.48 Total impact

• Article: A µ‐dependent approach to H∞ control of uncertain switched linear systems with average dwell time

  Lixian Zhang, El-Kebir Boukas, Peng Shi, Zhaobo Chen
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  ABSTRACT: This paper concerns H∞ control problem for a class of discrete-time uncertain switched linear systems with average dwell time. The stability result for general discrete-time switched systems is first explored, and a µ-dependent approach is then introduced for the considered systems to the H∞ controller solution. A mode-dependent state-feedback controller is designed such that the resulting closed-loop system is robust exponentially stable and has a prescribed exponential H∞ performance index. The µ-dependent existence conditions of desired controller and admissible switching signals are derived and formulated in terms of linear matrix inequalities (LMIs). A numerical example is given to demonstrate the effectiveness of the developed theoretical results. Copyright © 2009 John Wiley & Sons, Ltd.
  Optimal Control Applications and Methods 12/2009; 32(1):15 - 27. · 0.65 Impact Factor
• Article: μ-Dependent model reduction for uncertain discrete-time switched linear systems with average dwell time

  Lixian Zhang, El-Kebir Boukas, Peng Shi
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  ABSTRACT: In this article, the model reduction problem for a class of discrete-time polytopic uncertain switched linear systems with average dwell time switching is investigated. The stability criterion for general discrete-time switched systems is first explored, and a μ-dependent approach is then introduced for the considered systems to the model reduction solution. A reduced-order model is constructed and its corresponding existence conditions are derived via LMI formulation. The admissible switching signals and the desired reduced model matrices are accordingly obtained from such conditions such that the resulting model error system is robustly exponentially stable and has an exponential H∞ performance. A numerical example is presented to demonstrate the potential and effectiveness of the developed theoretical results.
  International Journal of Control 01/2009; 82(2):378-388. · 0.98 Impact Factor
• Article: H

  Wudhichai Assawinchaichote, Sing Kiong Nguang, Peng Shi, El Kebir Boukas
  Mathematics and Computers in Simulation. 01/2008; 78:514-531.
• Article: H.

  Lixian Zhang, Peng Shi, El Kebir Boukas, Changhong Wang
  Automatica. 01/2008; 44:2944-2949.
• Article: Simultaneous ℋ︁2/ℋ︁∞ control of uncertain jump systems with functional time‐delays

  Magdi S. Mahmoud, Peng Shi, El Kebir Boukas, Lakhim Jain
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  ABSTRACT: This paper presents new results pertaining to the control design of a class of linear uncertain systems with Markovian jump parameters. An integral part of the system dynamics is a delayed state in which the time-delays are mode dependent. The jumping parameters are modelled as a continuous-time, discrete-state Markov process and the uncertainties are norm-bounded. We construct an appropriate Lyapunov–Krasovskii functional and design a simultaneous 2/∞ controller which minimizes a quadratic 2 performance measure while satisfying a prescribed ∞-norm bound on the closed-loop system. It is established that sufficient conditions for the existence of the simultaneous 2/∞ controller and the associated performance upper bound are cast in the form of linear matrix inequalities. Simulation results are provided and extension to the case where the jumping rates are subject to uncertainties is presented. Copyright © 2007 John Wiley & Sons, Ltd.
  International Journal of Robust and Nonlinear Control 05/2007; 18(3):296 - 318. · 1.55 Impact Factor
• Article: H∞ control of switched linear discrete‐time systems with polytopic uncertainties

  Lixian Zhang, Peng Shi, El-Kebir Boukas, Changhong Wang
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  ABSTRACT: In this paper, the problem of designing H∞ state-feedback controllers for switched linear discrete-time systems with polytopic uncertainties is investigated. Two approaches on designing robust and parameter-dependent H∞ controllers are proposed and the existence conditions of the desired controllers are derived and formulated in terms of a set of linear matrix inequalities. By solving the corresponding convex optimization problem, the desired controllers are obtained, respectively, and different optimal H∞ noise-attenuation level bounds of corresponding closed-loop systems are given as well. The designed controllers have their own advantages and disadvantages regarding the conservatism and realization complexity. An illustrative example emerging in networked control systems (NCS) and numerical simulations are presented to show the applicability and effectiveness of the obtained theoretic results. Copyright © 2006 John Wiley & Sons, Ltd.
  Optimal Control Applications and Methods 09/2006; 27(5):273 - 291. · 0.65 Impact Factor
• Article: Robust disturbance attenuation for discrete‐time active fault tolerant control systems with uncertainties

  Peng Shi, El Kebir Boukas, Sing Kiong Nguang, Xianping Guo
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  ABSTRACT: The problems of stochastic stability and stochastic disturbance attenuation for a class of linear discrete-time systems are considered in this paper. The system under study is a state space model possessing two Markovian jump parameters: one is failure process and another is failure detection and isolation scheme. A controller is designed to guarantee the stochastic stability and a disturbance attenuation level. Robustness problems for the above system with norm-bounded parameter uncertainties are also investigated. It is shown that the uncertain system can be robustly stochastically stabilized and have a robust disturbance attenuation level for all admissible perturbations if a set of coupled Riccati inequalities has solutions. A numerical example is given to show the potential of the proposed technique. Copyright © 2003 John Wiley & Sons, Ltd.
  Optimal Control Applications and Methods 04/2003; 24(2):85 - 101. · 0.65 Impact Factor
• Article: Robust control for Markovian jumping discrete-time systems.

  Peng Shi, El Kebir Boukas, Ramesh K. Agarwal
  Int. J. Systems Science. 01/1999; 30:787-797.
• Conference Proceeding: H∞ control for singularly perturbed systems in the presence of Markovian jump parameters

  V. Dragan, Peng Shi, El-Kebir Boukas
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  ABSTRACT: In this paper, we study the problem of H_∞ control for singularly perturbed linear continuous-time systems with Markovian jump parameters. On the basis of reduced order technique, our attention is focused on the designing of state feedback control such that both stochastic stability and a prescribed H_∞ performance for the full order system are achieved. It has been shown that the above problem can be solved if a set of coupled Riccati equations has solution. The asymptotic behaviour of the composite controller is analyzed when the singular perturbation is sufficiently small
  Decision and Control, 1997., Proceedings of the 36th IEEE Conference on; 01/1998
• Conference Proceeding: Disturbance Attenuation for Systems Governed by Markov Decision Processes.

  Peng Shi, El Kebir Boukas, Yan Shi, Ramesh K. Agarwal
  The Fifth International Conference on Neural Information Processing, ICONIP'R98, Kitakyushu, Japan, October 21-23, 1998, Proceedings; 01/1998
• Article: Stability and stabilization of continuous-time singular hybrid systems

  Yuanqing Xia, El-Kebir Boukas, Peng Shi, Jinhui Zhang
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  ABSTRACT: In this paper, the problems of stability and state feedback stabilization for a class of continuous-time singular hybrid systems are investigated. A new sufficient and necessary condition for a continuous-time singular hybrid system to be regular, impulse-free and stochastically stable is proposed in terms of a set of coupled strict linear matrix inequalities (LMIs). Moreover, a new sufficient and necessary condition is presented for the existence of the state feedback controller in terms of a set of coupled strict matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness of the obtained theoretical results.
  Automatica.
• Article: Control for discrete singular hybrid systems

  Yuanqing Xia, Jinhui Zhang, El-Kebir Boukas
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  ABSTRACT: The problems of stability, state feedback control and static output feedback control for a class of discrete-time singular hybrid systems are investigated in this paper. A new sufficient and necessary condition for a class of discrete-time singular hybrid systems to be regular, causal and stochastically stable is proposed in terms of a set of coupled strict linear matrix inequalities (LMIs). Sufficient conditions are proposed for the existence of state feedback controller and static output feedback controller in terms of a set of coupled strict LMIs, respectively. Finally, two illustrative examples are provided to demonstrate the applicability of the proposed approach.
  Automatica.
• Article: Robust H∞ control for linear Markovian jump systems with unknown nonlinearities

  El Kebir Boukas, Peng Shi, Sing Kiong Nguang
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  ABSTRACT: This paper studies the problem of stochastic stability and disturbance attenuation for a class of linear continuous-time uncertain systems with Markovian jumping parameters. The uncertainties are assumed to be nonlinear and state, control and external disturbance dependent. A sufficient condition is provided to solve the above problem. An H∞ controller is designed such that the resulting closed-loop system is stochastically stable and has a disturbance attenuation γ for all admissible uncertainties. It is shown that the control law is in terms of the solutions of a set of coupled Riccati inequalities. A numerical example is included to demonstrate the potential of the proposed technique.
  Journal of Mathematical Analysis and Applications.