Necessary and sufficient conditions for containment control of fractional-order multi-agent systems

Abstract

Abstract This paper addresses the containment control problems of fractional-order multi-agent systems, which have more extensive forms than the integer-order systems. Three cases are analyzed, including fractional-order single-integrator systems, fractional-order single-integrator systems with time-delays, and fractional-order double-integrator systems. For each case, a neighbor-based protocol with sampled information is proposed. Then the closed-loop systems, i.e., fractional-order continuous-time systems with sampled-data based protocols, are equivalently transformed into integer-order discrete-time systems by using the solution formula for fractional-order linear systems in each sampling interval. Some necessary and sufficient conditions are established to guarantee the achievement of containment control. When the order of fractional derivative takes the value α = 1 , the results reduce to the previous results on integer-order multi-agent systems. In addition, some examples are provided to validate the correctness of the main theorems.