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Necessary and Sufficient Condition for Robust Stability and Stabilizability of Continuous-Time Linear Systems with Markovian Jumps

Author

Listed:
  • O. L. V. Costa

    (University of Sao Paulo)

  • E. K. Boukas

    (Eacute;cole Polytechnique de Montréal and GERAD)

Abstract

In this paper, we investigate the quadratic stability and quadratic stabilizability of the class of continuous-time linear systems with Markovian jumps and norm-bound uncertainties in the parameters. Under some appropriate assumptions, a necessary and sufficient condition is established for mean-square quadratic stability and mean-square quadratic stabilizability of this class of systems. The quadratic guaranteed cost control problem is also addressed via a LMI optimization problem.

Suggested Citation

  • O. L. V. Costa & E. K. Boukas, 1998. "Necessary and Sufficient Condition for Robust Stability and Stabilizability of Continuous-Time Linear Systems with Markovian Jumps," Journal of Optimization Theory and Applications, Springer, vol. 99(2), pages 359-379, November.
    • Handle: RePEc:spr:joptap:v:99:y:1998:i:2:d:10.1023_a:1021722210476
    DOI: 10.1023/A:1021722210476
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    References listed on IDEAS

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    1. P. Shi & E. K. Boukas, 1997. "H ∞-Control for Markovian Jumping Linear Systems with Parametric Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 95(1), pages 75-99, October.
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    Cited by:

    1. Cañada, Héctor & Romera, Rosario, 2009. "Controlled diffusion processes with markovian switchings for modeling dynamical engineering systems," DES - Working Papers. Statistics and Econometrics. WS ws093714, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Yuan, Chenggui & Mao, Xuerong, 2004. "Convergence of the Euler–Maruyama method for stochastic differential equations with Markovian switching," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(2), pages 223-235.
    3. E.K. Boukas & Z.K. Liu & F. Al-Sunni, 2003. "Guaranteed Cost Control of a Markov Jump Linear Uncertain System Using a Time-Multiplied Cost Function," Journal of Optimization Theory and Applications, Springer, vol. 116(1), pages 183-204, January.
    4. O. L. V. Costa & J. C. C. Aya, 2001. "Temporal Difference Methods for the Maximal Solution of Discrete-Time Coupled Algebraic Riccati Equations," Journal of Optimization Theory and Applications, Springer, vol. 109(2), pages 289-309, May.

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