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A new class of positive linear systems consisting of n subsystems with different fractional orders is introduced. Solution to the set of matrix linear differential equations with different fractional orders is derived. Necessary and sufficient conditions for the positivity of the fractional systems are established. It is shown that the linear electrical circuits composed of resistors, supercondensators, coils, and voltage (current) sources are positive systems with different fractional orders.
Circuits and Systems I: Regular Papers, IEEE Transactions on (Volume:58 , Issue: 6 )
Date of Publication: June 2011