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 6 Professor C. Tomlin Department of Electrical Engineering and Computer Sciences, UC Berkeley Fall 2011 Issued 10/27; Due 11/4 Problem 1: Linear systems. Using the definitions of linear and timeinvariance discussed in class, show that: (a) x = A ( t ) x + B ( t ) u, y = C ( t ) x + D ( t ) u, x ( t ) = x is linear; (b) x = Ax + Bu, y = Cx + Du, x (0) = x is time invariant (its clearly linear, from the above). Here, the matrices in the above are as defined in class for multiple input multiple output systems. Problem 2: A linear timeinvariant system. Consider a singleinput, singleoutput, time invariant linear state equation x ( t ) = Ax ( t ) + bu ( t ) ,x (0) = x (1) y ( t ) = cx ( t ) (2) If the nominal input is a nonzero constant, u ( t ) = u , under what conditions does there exist a constant nominal solution x ( t ) = x , for some x ?...
View
Full
Document
This note was uploaded on 12/09/2011 for the course EE 221A taught by Professor Clairetomlin during the Fall '10 term at University of California, Berkeley.
 Fall '10
 ClaireTomlin
 Electrical Engineering

Click to edit the document details