hw2_6243_2003

# hw2_6243_2003 - Massachusetts Institute of Technology...

This preview shows pages 1–2. Sign up to view the full content.

± Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.243j (Fall 2003): DYNAMICS OF NONLINEAR SYSTEMS by A. Megretski Problem Set 2 1 Problem 2.1 Consider the feedback system with external input r = r ( t ), a causal linear time invariant forward loop system G with input u = u ( t ), output v = v ( t ), and impulse response g ( t ) = 0 . 1 ( t ) + ( t + a ) 1 / 2 e t , where a 0 is a parameter, and a memoryless nonlinear feedback loop u ( t ) = r ( t ) + ± ( v ( t )), where ± ( y ) = sin( y ). It is customary to require well- u r - - G - v ± ( y ) Figure 2.1: Feedback setup for Problem 2.1 posedness of such feedback models, which will usually mean existence and uniqueness of solutions v = v ( t ), u = u ( t ) of system equations t v ( t ) = 0 . 1 u ( t ) + h ( t π ) u ( π ) dπ, u ( t ) = r ( t ) + ± ( v ( t )) 0 on the time interval t [0 , ) for every bounded input signal r = r ( t ). 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 11/07/2011 for the course AERO 16.36 taught by Professor Alexandremegretski during the Spring '09 term at MIT.

### Page1 / 3

hw2_6243_2003 - Massachusetts Institute of Technology...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online