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Unformatted text preview: T is a constant torque. Let B r = { x ∈ R 2 :  x  < r } . ²or this system (represented as ˙ x = f ( x )) Fnd whether f is locally Lipschitz in x on B r for su³ciently small r , locally Lipschitz in x on B r for any Fnite r , or globally Lipschitz in x (ie. Lipschitz for all x ∈ R 2 ). Problem 3: Perturbed nonlinear systems. Suppose that some physical system obeys the di±erential equation ˙ x = p ( x, t ) , x ( t ) = x , ∀ t ≥ t where p ( · , · ) obeys the conditions of the fundamental theorem. Suppose that as a result of some perturbation the equation becomes ˙ z = p ( z, t ) + f ( t ) , z ( t ) = x + δx , ∀ t ≥ t Given that for t ∈ [ t , t + T ],  f ( t )  ≤ ǫ 1 and  δx  ≤ ǫ , Fnd a bound on  x ( t )z ( t )  valid on [ t , t + T ]. 1...
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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
 ClaireTomlin
 Electrical Engineering

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