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This paper considers the solution to a class of the second-order Sylvester matrix equation EVF2−AVF−CV=BW. 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

mathematical problems in engineering

On the Parametric Solution to the Second-Order Sylvester Matrix Equation<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>E</mml:mi><mml:mi>V</mml:mi><mml:msup><mml:mi>F</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo>−</mml:mo><mml:mi>A</mml:mi><mml:mi>V</mml:mi><mml:mi>F</mml:mi><mml:mo>−</mml:mo><mml:mi>C</mml:mi><mml:mi>V</mml:mi><mml:mo>=</mml:mo><mml:mi>B</mml:mi><mml:mi>W</mml:mi></mml:mrow></mml:math>

On the Parametric Solution to the Second-Order Sylvester Matrix EquationEVF2−AVF−CV=BW