Summary: ELEC 302 Solutions: HW #6
Problem [1]. As in problem [1] of the previous assignment, consider the RLC system with the following
values of the parameters: C1 = C2 = 1, R = R1 = R2 = 1, L1 = L2 = 1. Consider also the states:
^x = [1 0 0 0]T
, ~x = [0 0 0 1]T
(a) Compute the infinite reachability gramian. (b) Hence find the state which is the easiest and most
difficult to reach. (c) Find an input which will steer the system from 0 to ^x in an infinite amount of time.
Repeat for ~x. What is the required energy in each case? Plot the two inputs on the same graph.
Solution. Recall that
A =




-1 -1 -1 0
1 -1 0 0
-1 0 -1 -1
0 0 1 -1

Source: Antoulas, Athanasios C. - Department of Electrical and Computer Engineering, Rice University

Collections: Engineering