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Unformatted text preview: EE221A Linear System Theory Problem Set 3 Professor C. Tomlin Department of Electrical Engineering and Computer Sciences, UC Berkeley Fall 2007 Issued 9/27; Due 10/4 Problem 1: Dynamical systems, time invariance. Suppose that the output of a system is represented by y ( t ) = integraldisplay t- e- ( t- ) u ( ) d Show that it is a (i) dynamical system, and that it is (ii) time invariant. You may select the input space U to be the set of bounded, piecewise continuous, real-valued functions defined on (- , ). Problem 2: Satellite Problem, linearization, state space model. Model the earth and a satellite as particles. The normalized equations of motion, in an earth-fixed inertial frame, simplified to 2 dimensions (from Lagranges equations of motion, the Lagrangian L = T- V = 1 2 r 2 + 1 2 r 2 2- k r ): r = r 2- k r 2 + u 1 =- 2 r r + 1 r u 2 with u 1 ,u 2 representing the radial and tangential forces due to thrusters. The reference orbit withrepresenting the radial and tangential forces due to thrusters....
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- Fall '10
- Electrical Engineering