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Unformatted text preview: also showed, through extension of equalities, that the same conclusion holds even if A is not semi-simple. (b) By (a), there is a unique symmetric solution to the equation. Let P = R e A T t Qe At dt . Then P > 0 since x T Px = R ( e At x ) T Q ( e At x ) dt and the integrand is > 0 whenever x 6 = 0 since e At is nonsingular and Q > 0. Further, P solves the equation since A T P + PA = Z d dt e A T t Qe At dt =-Q. Exercise 4. (a) ( s ) = s 2 + (4 + 2 f 2 + f 1 ) s + (6 f 1 + 7 f 2-7). (b) ( s ) = s 2 + (7 k + 4) s + (27 k-7). Exercise 5. k = ( a 1- 1 a 2- 2 a 3- 3 ) yields the desired characteristic equation....
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This note was uploaded on 04/11/2011 for the course EE 221A taught by Professor Clairetomlin during the Fall '10 term at University of California, Berkeley.
- Fall '10