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Unformatted text preview: EE221A Linear System Theory Problem Set 4 Professor C. Tomlin Department of Electrical Engineering and Computer Sciences, UC Berkeley Fall 2011 Issued 9/30; Due 10/7 Problem 1: Existence and uniqueness of solutions to differential equations. Consider the following two systems of differential equations: x 1 =- x 1 + e t cos( x 1- x 2 ) x 2 =- x 2 + 15 sin( x 1- x 2 ) and x 1 =- x 1 + x 1 x 2 x 2 =- x 2 (a) Do they satisfy a global Lipschitz condition? (b) For the second system, your friend asserts that the solutions are uniquely defined for all possible initial conditions and they all tend to zero for all initial conditions. Do you agree or disagree? Problem 2: Existence and uniqueness of solutions to linear differential equations. Let A ( t ) and B ( t ) be respectively n n and n n i matrices whose elements are real (or complex) valued piecewise continuous functions on R + . Let u ( ) be a piecewise continuous function from R + to R n i . Show that for any fixed u (...
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This note was uploaded on 12/09/2011 for the course EE 221A taught by Professor Clairetomlin during the Fall '10 term at University of California, Berkeley.
- Fall '10
- Electrical Engineering