problem4

problem4 - EE221A Linear System Theory Problem Set 4...

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

View Full Document Right Arrow Icon
EE221A Linear System Theory Problem Set 4 Professor C. Tomlin Department of Electrical Engineering and Computer Sciences, UC Berkeley Fall 2006 Issued 10/9; Due 10/18 Dear 221A folks: Some problems like the ones below may be included on the midterm on October 16. Thus, you may hand in your homework solutions to me on Monday October 15 and receive solutions to use in your midterm preparation. Problem 1: A linear time-invariant system. Consider a single-input, single-output, time invariant linear state equation ˙ x ( t ) = Ax ( t ) + bu ( t ) ,x (0) = x 0 (1) y ( t ) = cx ( t ) (2) If the nominal input is a non-zero constant, u ( t ) = u , under what conditions does there exist a constant nominal solution x ( t ) = x 0 , for some x 0 ? Under what conditions is the corresponding nominal output zero? Under what conditions do there exist constant nominal solutions that satisfy y = u for all u ? Problem 2. Preservation of Eigenvalues under Similarity Transform. Consider a matrix
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 12/09/2011 for the course EE 221A taught by Professor Clairetomlin during the Fall '10 term at Berkeley.

Page1 / 2

problem4 - EE221A Linear System Theory Problem Set 4...

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