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Mean Square Exponential Stability of Stochastic Switched System with Interval Time‐Varying Delays

Author

Listed:
  • Manlika Rajchakit
  • Grienggrai Rajchakit

Abstract

This paper is concerned with mean square exponential stability of switched stochastic system with interval time‐varying delays. The time delay is any continuous function belonging to a given interval, but not necessary to be differentiable. By constructing a suitable augmented Lyapunov‐Krasovskii functional combined with Leibniz‐Newton’s formula, a switching rule for the mean square exponential stability of switched stochastic system with interval time‐varying delays and new delay‐dependent sufficient conditions for the mean square exponential stability of the switched stochastic system are first established in terms of LMIs. Numerical example is given to show the effectiveness of the obtained result.

Suggested Citation

  • Manlika Rajchakit & Grienggrai Rajchakit, 2012. "Mean Square Exponential Stability of Stochastic Switched System with Interval Time‐Varying Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:623014
    DOI: 10.1155/2012/623014
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    References listed on IDEAS

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    1. Irada A. Dzhalladova & Jaromír Baštinec & Josef Diblík & Denys Y. Khusainov, 2011. "Estimates of Exponential Stability for Solutions of Stochastic Control Systems with Delay," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    2. Irada A. Dzhalladova & Jaromír Baštinec & Josef Diblík & Denys Y. Khusainov, 2011. "Estimates of Exponential Stability for Solutions of Stochastic Control Systems with Delay," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-14, May.
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    Cited by:

    1. P. Niamsup & G. Rajchakit, 2013. "New Results on Robust Stability and Stabilization of Linear Discrete‐Time Stochastic Systems with Convex Polytopic Uncertainties," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    2. Sendren Sheng-Dong Xu & Chih-Chiang Chen, 2013. "On Existence of Stabilizing Switching Laws within a Class of Unstable Linear Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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