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Stabilization on input time-varying delay for linear switched systems with truncated predictor control

  • * Corresponding author: A. Vinodkumar

    * Corresponding author: A. Vinodkumar

This work was supported by Science & Engineering Research Board (DST-SERB) project file number: ECR/ 2015/000301 in India

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  • This study is concerned with the stabilization problem for input time-varying delay switched system under the truncated predictor control scheme. The delay in the prediction feedback, is subjected by predicting the future trajectory of the states by system equations and initial conditions, which is known as truncated prediction feedback (TPF). The TPF is used to construct the state feedback law for stabilizing the linear switched system. By constructing Lyapunov-Krasovskii functions and, the stability condition is derived to ensure the globally asymptotically stable of the state feedback stabilization at the origin. When switching system is unstable, truncated predictor control method and Hurwitz convex combination makes the system stable. Finally, a numerical example and their simulation results are given to show the effectiveness of the proposed approach.

    Mathematics Subject Classification: 93C30, 93D15, 93B52, 37M99.


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  • Figure 1.  Unstable behavior mode:1 of the linear system $ (16) $

    Figure 2.  Unstable behavior mode:2 of the linear system $ (16)$

    Figure 3.  Phase plot mode:1 of the systems $ (16) $ with initial condition $ x(t) = [0.3, 0.1]^{T} $

    Figure 4.  Phase plot mode:2 of the systems $ (16) $ with initial condition $ x(t) = [0.3, 0.1]^{T} $

    Figure 5.  Stability for the mode:1 of system $ (16) $ with initial condition $ x(t) = [0.3, 0.1]^{T} $

    Figure 6.  Stability for the mode:2 of system $ (16) $ with initial condition $ x(t) = [0.3, 0.1]^{T} $

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