hw2_6243_2003

hw2_6243_2003 - Massachusetts Institute of Technology...

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

View Full Document Right Arrow Icon
± 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
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
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 Right Arrow Icon
Ask a homework question - tutors are online