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Unformatted text preview: ) , T > x (0) = 1 (1) • What is the form of the function f in (1)? • Is your f Lipshitz continuous with respect to x ? Explain. • In order to solve (1) apply the Picard iteration. Does it converge and if yes to what? Problem 3 : Let A = p a 1 a P for some scalar a n = 0. ±ind e tA . September 3, 2009 2 Problem 4 : Consider the system ˙ x ( t ) = A ( t ) x ( t ) where A ( t ) = λ λt λ λt λ • What are the eigenvalues of A ( t )? • How many eigenvectors are associated with the eigenvalues of A ( t )? • Find the state transition matrix for the system. Problem 5 : Let T be a positive scalar and A a square n × n matrix. Find a concise expression fre i T e tA dt ....
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- Spring '10