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On the Parametric Solution to the Second-Order Sylvester Matrix Equation E V F 2 − A V F − C V = B W

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  • Wang Guo-Sheng
  • Lv Qiang
  • Duan Guang-Ren

Abstract

This paper considers the solution to a class of the second-order Sylvester matrix equation E V F 2 − A V F − C V = B W . Under the controllability of the matrix triple ( E , A , B ) , a complete, general, and explicit parametric solution to the second-order Sylvester matrix equation, with the matrix F in a diagonal form, is proposed. The results provide great convenience to the analysis of the solution to the second-order Sylvester matrix equation, and can perform important functions in many analysis and design problems in control systems theory. As a demonstration, an illustrative example is given to show the effectiveness of the proposed solution.

Suggested Citation

  • Wang Guo-Sheng & Lv Qiang & Duan Guang-Ren, 2007. "On the Parametric Solution to the Second-Order Sylvester Matrix Equation E V F 2 − A V F − C V = B W," Mathematical Problems in Engineering, Hindawi, vol. 2007, pages 1-16, November.
    • Handle: RePEc:hin:jnlmpe:021078
    DOI: 10.1155/2007/21078
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