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Switched Nonlinear Systems with Distributed Parameters

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Stabilization of Switched Nonlinear Systems with Unstable Modes

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 9))

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Abstract

The SNS considered in Chaps. 2–5 are driven by ordinary differential equations. When there exist distributed parameters, partial differential equations (PDE) are taken instead of ODE to describe the dynamics of each mode. This chapter considers two typical switched PDE models: switched hyperbolic systems (Sect. 6.1) and Switched parabolic systems (Sect. 6.2). The stabilization design fully combines the methods for switched ODE and the characteristics of PDE.

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Notes

  1. 1.

    In many physical systems described by (6.1) with boundary condition (6.2), \(\xi (t,\cdot )\) is non-negative, the elements \(K\) are also non-negative. We only consider \(\xi \in \mathfrak {R}^n_{\ge 0}\) and \(K\in \mathfrak {R}^{n\times n}_{\ge 0}\). The results can be straightly extended to the case \(\xi \in \mathfrak {R}^n_{\le 0}\).

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Author information

Authors and Affiliations

  1. College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China

    Hao Yang & Bin Jiang

  2. LAGIS, UMR CNRS 8219, Université de Lille 1 Sciences et Technologies, Villeneuve d’Ascq cedex, France

    Vincent Cocquempot

Authors
  1. Hao Yang
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  2. Bin Jiang
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  3. Vincent Cocquempot
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Correspondence to Hao Yang .

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Yang, H., Jiang, B., Cocquempot, V. (2014). Switched Nonlinear Systems with Distributed Parameters. In: Stabilization of Switched Nonlinear Systems with Unstable Modes. Studies in Systems, Decision and Control, vol 9. Springer, Cham. https://doi.org/10.1007/978-3-319-07884-7_6

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  • DOI: https://doi.org/10.1007/978-3-319-07884-7_6

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