  Stability and stabilization analysis of fractional-order linear
time-invariant (FO-LTI) systems with different derivative orders is studied in
this paper. First, by using an appropriate linear matrix function, a
single-order equivalent system for the given different-order system is
introduced by which a new stability condition is obtained that is easier to
check in practice than the conditions known up to now. Then the stabilization
problem of fractional-order linear systems with different fractional orders via
a dynamic output feedback controller with a predetermined order is
investigated, utilizing the proposed stability criterion. The linear matrix
inequality based procedure of developing stabilizing output feedback control is
preserved in spite of the complexity of assuming the most complete linear
controller model, with direct feedthrough parameter. The proposed stability and
stabilization theorems are applicable to FO-LTI systems with different
fractional orders in one or both of and intervals. Eventually, some numerical
examples are presented to confirm the obtained analytical results.
