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Unformatted text preview: EE221A Linear System Theory Problem Set 5 Professor C. Tomlin Department of Electrical Engineering and Computer Sciences, UC Berkeley Fall 2010 Issued 10/8; Due 10/15 You may pick up solutions from us on 10/14, 10/15 or 10/18, after you hand in your homework, so that you have them for your midterm review. Problem 1: Dynamical systems, time invariance. Suppose that the output of a system is represented by y ( t ) = integraldisplay t −∞ e − ( t − τ ) u ( τ ) dτ 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 Lagrange’s equations of motion, the Lagrangian L = T- V = 1 2 ˙ r 2 + 1 2 r 2 ˙ θ 2- k r ): ¨ r = r ˙...
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- Fall '10
- Electrical Engineering, ·, Department of Electrical Engineering and Computer Sciences, Professor C. Tomlin, matrix diﬀerential equation