Suppose that H1(s) and H2(s) are two strictly proper singleinput, single-output transfer functions with controllable statespace realizations (A1, B1, C1) and (A2, B2, C2), respectively. Construct a state-space realization for the parallel interconnection H1(s) H2(s), and use the Popov-Belevitch-Hautus eigenvector test to show that the parallel realization is controllable if and only if A1 and A2 have no common eigenvalues.

Acompressor compresses a gas, a pump compresses a liquid. for a given pressure ratio, why does it take more work to compress a gas in a compressor than a liquid in a pump? a)- for a given pressure ratio the average specific volume for a gas is much higher than the average specific volume for a liquid. b)- there is no difference. the only difference is the amount of heat generated (not work) c)- for a given pressure ratio the average volurge for a gas is much higher than the average volume for a liquid. d)-there is no difference