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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 time-invariance 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 time-invariant system. Consider a single-input, single-output, 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 non-zero constant, u ( t ) = u , under what conditions does there exist a constant nominal solution x ( t ) = x , for some x ?...
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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 University of California, Berkeley.
- Fall '10
- Electrical Engineering