problem9

# problem9 - EE221A Linear System Theory Problem Set 9...

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EE221A Linear System Theory Problem Set 9 Professor C. Tomlin Department of Electrical Engineering and Computer Sciences, UC Berkeley Fall 2007 Issued 12/4; Due 12/15 221A folks: Homework 9 is due at the Fnal exam. However, if you’d like to hand in your homework early and receive solutions, we’ll have solutions ready by Wednesday December 10. Problem 1. Two linear time invariant systems S 1 ( A 1 ,B 1 ,C 1 ,D 1 ) and S 2 ( A 2 ,B 2 ,C 2 ) are interconnected as shown in the Figure 1. Find state space equations for the composite system with inputs u 1 ,u 2 and outputs y 1 ,y 2 . Prove that if S 1 ,S 2 are stabilizable and detectable, then the composite system is also stabilizable and detectable. Problem 2: Inertial navigation. The equations for errors in an inertial navigation system are approximated by: ˙ δx = δv ˙ δv = - gδψ + E A ˙ δψ = 1 R δv + E G where δx is the position error, δv is the velocity error, δψ is the tilt of the platform, g is the acceleration due to gravity, and

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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 Berkeley.

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problem9 - EE221A Linear System Theory Problem Set 9...

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