Analytic study on a state observer synchronizing a class of linear fractional differential systems

• In the classical sense, the characteristic equation of the fractional differential equation is obtained.
• The sufficient and necessary condition of poles assignment for the fractional differential system is derived.
• A counterexample is provided.

This paper is concerned with Theorem 2 in Matignon and d’André-Novel (1997) [1], which was sufficient and necessary criterion on a state observer for a class of linear fractional differential systems. Based on the stability theory, the dual principle and the pole assignment theory of the fractional differential system, we have proved the validity of sufficiency of Theorem 2 in details. A counterexample is provided to show that the condition of Theorem 2 is not necessary.