This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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, realvalued 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 earthfixed 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....
View Full
Document
 Fall '10
 ClaireTomlin
 Electrical Engineering

Click to edit the document details