26 - sssolution26 filled

26 - sssolution26 filled - ME 575 Handouts Complex...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
ME 575 Handouts 1 ME575 Session 26: Solution of State Space Equations School of Mechanical Engineering Purdue University Slide 1 Complex Eigenvalues Complex Eigenvalues Assume A matrix has complex eigenvalues: matrix has complex eigenvalues: Eigenvectors: Eigenvectors: To transform to real eigenvectors: To transform to real eigenvectors: 12 j, j λ =σ+ ω λ =σ− ω xj , =α+ β =α− β m let T = αβ 11 A x (j ) x A ) ) ) =σ+ω ⇒ α+β=σ+ωα+β A σ ω ⎡⎤ αβ=αβ ⎣⎦ ωσ ME575 Session 26: Solution of State Space Equations School of Mechanical Engineering Purdue University Slide 2 Example of Complex Eigenvalues Example of Complex Eigenvalues 01 A : 52 = ⎢⎥ −− 2 1 A 25 0 λ λ −= = λ + λ + = λ+ I 1j 2 : λ=− +
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
ME 575 Handouts 2 ME575 Session 26: Solution of State Space Equations School of Mechanical Engineering Purdue University Slide 3 Alternative Formulation Alternative Formulation ME575 Session 26: Solution of State Space Equations School of Mechanical Engineering Purdue University Slide 4 Solution of LTI State Equations Solution of LTI State Equations Free Response (u = 0): Free Response (u = 0): equate like powers of t equate like powers of t xA x = ± 2k 01 2 k x(t) t t t
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 8

26 - sssolution26 filled - ME 575 Handouts Complex...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online