Necessary and sufficient conditions of observer-based stabilization for a class of fractional-order descriptor systems

This paper is concerned with observer-based stabilization for fractional-order descriptor systems with order 1≤α<2. A necessary and sufficient condition is proposed for the control design by using appropriate matrix variable decoupling technique. The developed results are more general and useful than some existing works, and cover them as special cases, in which only sufficient conditions were presented, in particular, for normal fractional-order systems. Illustrative examples are provided to verify and demonstrate the effectiveness and potential of the theoretic results obtained.