Control ENG HW_Part_62

Control ENG HW_Part_62 - .x + σ =X Characteristic equation...

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Unformatted text preview: .x + σ =X Characteristic equation becomes a 0 ( X − σ ) n + a1 ( X − σ ) n −1 + ................................. + a n = 0 Hence if we apply Routh criteria, We will actually be looking for roots with real part > σ rather than >0 a 0 x n + a1 x n −1 + a 2 x n −2 ................................. + a n = 0 Routh criterion detects if any root α j is greater than zero. Is there any x = α 1 , α 2 ,...............,α j ,..........α n > 0 − − − − − (1) Now we want to detect any root α j > −σ α j> 0 From(1) x = α 1 , α 2 ,............................α j ,..........................α n , > 0 implies is there any x = α1 > 0 x = α2 > 0 . . . x =αj >0 . . . x = αn > 0 add σ on both sides is there any x + σ = α1 + σ > 0 x +σ = α2 +σ > 0 . . . .x + σ = α j + σ > 0 . . . x +σ = αn +σ > 0 so, Let X = x + σ and apply Routh criteria to det ect any α j + σ > 0 or α j > −σ 14.7 Show that any complex no S1 satisfying S < 1, yields a value of Z= 1+ s that satisfies Re(Z)>0, 1− s Let S=x+iy, x2 + y2 < 1 ...
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This note was uploaded on 11/13/2011 for the course COP 4355 taught by Professor Koslov during the Spring '10 term at University of Florida.

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Control ENG HW_Part_62 - .x + σ =X Characteristic equation...

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