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Saturated control design for linear differential inclusions subject to disturbance

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Abstract

In this paper, saturated control design method is presented for robust stabilization of linear differential inclusions subject to disturbance. Convex hull quadratic Lyapunov functions are used to construct nonlinear state feedback laws. By the state feedbacks, stabilization, disturbance rejection with minimal reachable set and least L 2 gain are achieved simultaneously. Finally, the effectiveness of the proposed scheme is illustrated by a simulative example.

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References

  1. Boyd, S., EI Ghaoui, L., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in Systems and Control Theory. SIAM Studies in Applied Mathematics. SIAM, Philadelphia (1994)

    Google Scholar 

  2. Smirnov, G.V.: Introduction to the Theory of Differential Inclusions. Graduate Studies in Mathematics. SIAM, Philadelphia (2002)

    MATH  Google Scholar 

  3. Sun, Y.: Stability criteria for a class of differential inclusion systems with discrete and distributed time delays. Chaos Solitons Fractals (2007). doi:10.1016/j.chaos.2007.07.002

    Google Scholar 

  4. Chen, J.: Asymptotic stability for tracking control of nonlinear uncertain dynamical systems described by differential inclusions. J. Math. Anal. Appl. 261, 369–389 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  5. Zevin, A., Pinsky, M.: General solution of stability problem for plane linear switched systems and differential inclusions. IEEE Trans. Autom. Control 53, 2149–2153 (2008)

    Article  MathSciNet  Google Scholar 

  6. Blanchini, F., Megretski, A.: Robust state feedback control of LTV systems: Nonlinear is better than linear. IEEE Trans. Autom. Control 44, 802–807 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  7. Hu, T., Lin, Z.: Composite quadratic Lyapunov functions for constrained control systems. IEEE Trans. Autom. Control 48, 440–450 (2003)

    Article  MathSciNet  Google Scholar 

  8. Hu, T.: Nonlinear control design for linear differential inclusions via convex hull of quadratics. Automatica 43, 685–692 (2007)

    Article  MATH  Google Scholar 

  9. Goebel, R., Teel, A., Hu, T., Lin, Z.: Conjugate convex Lyapunov functions for dual linear differential equations. IEEE Trans. Autom. Control 51, 661–666 (2006)

    Article  MathSciNet  Google Scholar 

  10. Hu, T., Teel, A., Zaccarian, L.: Stability and performance for saturated systems via quadratic and nonquadratic Lyapunov functions. IEEE Trans. Autom. Control 51, 1770–1786 (2006)

    Article  MathSciNet  Google Scholar 

  11. Hu, T., Lin, Z., Chen, B.: An analysis and design method for linear systems subject to actuator saturation and disturbance. Automatica 38, 351–359 (2002)

    Article  MATH  Google Scholar 

Download references

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Authors and Affiliations

  1. College of Mathematics, Physics, and Information Engineering, Zhejiang Normal University, Jinhua, 321004, China

    Xiushan Cai

  2. School of Electronic, Information and Electrical Engineering, Shanghai Jiaotong University, Shanghai, 200240, China

    Leipo Liu & Wei Zhang

Authors
  1. Xiushan Cai
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  2. Leipo Liu
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  3. Wei Zhang
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Corresponding author

Correspondence to Xiushan Cai.

Additional information

This work is partially supported by the National

Natural Science Foundation of China (No. 60774011),

the Natural Science Foundation of Zhejiang Province in

China (No. Y105141), and the Natural Science Foundation

of Fujian Province in China (No. 2008J0026).

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Cai, X., Liu, L. & Zhang, W. Saturated control design for linear differential inclusions subject to disturbance. Nonlinear Dyn 58, 487–496 (2009). https://doi.org/10.1007/s11071-009-9494-z

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  • DOI: https://doi.org/10.1007/s11071-009-9494-z

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