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Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Pls send me solution fast within 20 min and i will rate instantly!! Solution must be in typed form!!
Problem 4. Consider the p-input state equations x= Ax+ Bu. Suppose there exists a transformation matrix T such that B₁1 TB = and TAT = [4₁1 412 A₁₁ Where matrix B, has n, rows and rank (B₁)= n,, and matrix A₁, is n, xn,. The other submatrices are correspondingly dimensioned. Suppose also that rank (B) = rank (B₁). Show that the pair (A,B) is controllable if and only if the pair (A22, A2) is controllable.
Transcribed Image Text:Problem 4. Consider the p-input state equations x= Ax+ Bu. Suppose there exists a transformation matrix T such that B₁1 TB = and TAT = [4₁1 412 A₁₁ Where matrix B, has n, rows and rank (B₁)= n,, and matrix A₁, is n, xn,. The other submatrices are correspondingly dimensioned. Suppose also that rank (B) = rank (B₁). Show that the pair (A,B) is controllable if and only if the pair (A22, A2) is controllable.
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